1. If you want to create a cone or cylinder by spinning a 2–dimensional shape about an axis of symmetry, what shapes would you need to use?

2. Describe how the volume formulas for a cone, cylinder and pyramid derived. What are the similarities between the volume of a cone and pyramid?

3. What is the relationship between mass, density and volume? Provide and example that involves calculating population density.

4. Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimensions of common geometric shapes (prisms, cylinders, cones and spheres) will affect the volume of these shapes.

5. The concept of volume is something you experience everyday in your life. Provide a specific example in which you could solve a real-world application using volume

Answers

Answer 1

1) The answer for both includes a circle. You would rotate the shape around the axis of symmetry, creating an infinite number of 2-d circles stacked on top of each other, creating the cone or cylinder. In the case of a cylinder, the other shape is a rectangle, and in the case of a cone, a right triangle with one line serving as the axis of symmetry.

2) The volume of a cone is the area of the base, multiplied by height, divided by 3. This means that the volume of a cone is 1/3 the volume of a cylinder of equal height and base area. The volume of a cylinder is the area of the base times height. The volume of a pyramid, similar to a cone, is the area of the base (length x width) times the height, divided by three.

3) One definition of density is mass/volume, or mass per unit of volume. For example, if a 5 kg object has a volume of 10 cm³, than the density would be 0.5kg/cm³. In population density, relative to our example, area takes the place of volume and population takes the place of mass. This means that population density is population/area. For example, if 10,000 people occupy an area of 5 square miles, then the population density is 2,000 people/ square mile.

4) As you are clearly learning in this class, the volume of an object is not only determined by its dimensions, such as base, width, and height, but its shape. Let's review the cone example. If a cone and a cylinder have the same base area and height, the cone has a volume of 1/3 that of the cylinder.

5) When might you want to use volume in your daily life? Here is a depressing example. Say your corporate job in the Accounting Department has you feeling blue, and your only break is your daily trip to the water cooler. The cups at the cooler are cone-shaped. Not only is this inconvenient because you can't stand them up without getting the rim dirty, but these cups contain 1/3 the water that a perfectly cylindrical cup of the same base/height could provide. You may tell your manager this, and earn yourself some fancy new cylindrical paper cups!

Answer 2

Answer: if a cone and a cylinder have the same base and same height then the volume of the cone is the volume of the cylinder.

Step-by-step explanation: its right edge 2021

Related Questions

The graph shows a rectangle that has been rotated. Which statement is FALSE?

Answers

We need the question and the statements in order to know

It’s D cuz after rotation I don’t think it’ll still be in the same position

When the smaller of two consecutive integers is added to three three times the larger, the result is 23. find the integers?

Answers

consecutive integers are numbers in order, 1,2,3,4,5,6,....
if you make x the smaller number the next number will be (x+1).
x +3(x+1) = 23
x +3x +3 = 23
5x = 23 - 3
5x = 20
x = 20/5
x = 4

the smaller integer is 4 then the next is 5

The value of the integers can be obtained by solving the equation as 5 and 6 respectively.

What is a linear equation?

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

Suppose the smaller integer be x.

Then, the larger one is x + 1.

As per the question, the following equation can be formed as,

x + 3(x + 1) = 23

⇒ 4x + 3 = 23

⇒ x = 5

Thus, the larger integer is 5 + 1 = 6.

Hence, the integers are obtained as 5 and 6 respectively.

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how do you put 2.303,2.3,2.33 and 2.03 from least to greatest

Answers

you add extra zeroes until all numbers have the same quantity. in this case, 2.303 has three numbers after the decimal, so the other three number need it too. 2.300, 2.330, and 2.030. now that you have all of them looking the same now, you can tell which is least and work from there: 2.030 is the least, then 2.300, 2.303 then 2.330 is the largest.

The number can be arranged from least to greatest as 2.03<2.3<2.303<2.33.

What are decimal Numbers?

A decimal is a number with a whole and a fractional portion. Decimal numbers are between integers and indicate numerical value for a whole plus some fraction of a whole. In fraction form, we may say there is one and one-half pizzas. This is represented in decimal form as 1.5 pizzas.

Let's write the numbers to the third decimal point. Therefore, we can write the numbers as,

2.303 = 2.3032.3 = 2.3002.33 = 2.3302.03 = 2.030

Now, the numbers can be arranged as,

2.030 < 2.300 < 2.303 < 2.330

2.03 < 2.3 < 2.303 < 2.33

Hence, the number can be arranged from least to greatest as 2.03<2.3<2.303<2.33.

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Solve each proportion. Show your work.

a . 2x/7 = 12/14

b. 3/x-1 = 5/7

Answers

2x / 7 = 12 / 14

Start by cross multiplying

28x = 84

Divide both sides by 28

x = 3

b) 3 / x - 1 = 5 / 7

Start by cross multiplying

21 = 5x - 5

Flip the equation

5x - 5 = 21
+5 +5

5x = 26

x = 26/5

What is the measure of each of the following angles? If m

Answers

it would be 45 degrees as it is on a straight line

id say about 30-45*

a-b+2c=7
b+c=1
a-2b-3c=0

Answers

Equation 1) a - b + 2c = 7
Equation 2) b + c = 1
Equation 3) a - 2b - 3c = 0

Subtract equation 3 from equation 1.

3) a - 2b - 3c = 0
1) a - b + 2c = 7

Subtract equations from one another.

-b - 5c = -7 {This will now be called equation 4)

Then, add equation 4 into equation 2.

4) -b - 5c = -7
2) b + c = 1

Add.

-4c = -6

Divide both sides by -4.

c = 3/2

Plug in 3/2 for c in the 2nd equation.

2) b + c = 1

b + (3/2) = 1

Subtract 3/2 from both sides.

b = 1 - 3/2

Simplify.

b = 1 - 1 1/2

Simplify.

b = -1/2

Plug in -1/2 for b in equation 1 so that we find the value of a.

*Remember : b = -1/2, c = 3/2

1) a + b + 2c = 7

Plug in -1/2 for b, and plug in 3/2 for c.

a + (-1/2) + 2(3/2) = 7

Simplify.

a - 1/2 + 3 = 7

Simplify.

a - 2 1/2 = 7

Add 2 1/2 to both sides.

a = 7 + 2 1/2

Simplify.

a = 9 1/2

So, a = 9 1/2, b = -1/2, c = 3/2

~Hope I helped!~

Which statement best describes why the sale price is a function of the original price

Answers

what ever is the variable between the original sale and the sale price . meaning whats the diffrence how much did the price rise or lower

What is the solution to 89+k=-42

Answers

subtract 89 from -42. k=-131

89+k=-42

We simplify the equation to the form, which is simple to understand
89+k=-42

We move all terms containing k to the left and all other terms to the right.
+1k=-42-89

We simplify left and right side of the equation.
+1k=-131

We divide both sides of the equation by 1 to get k.
k=-131.

Which of these is correct?
A) 30,792 is greater than 31,875.
B) 31,875 is greater than 32,496.
C) 31,875 is greater than 30,792.
D) 32,496 is less than 31,875.

Answers

The correct answer is: [C]: " 31,875 is greater than 30,792. "
__________________________________________________________

During a sale at a bookstore, a customer buys one book at full price. The customer is given a 25 percent discount on a second book of equal or less value. If George buys two books that value full prices of $17 and $8, by what percent is the total cost of the two books reduced during the sale?

Answers

Amount paid for the first book is $17.

Amount paid for the second book is 0.75 x 8 = $6

Total amount paid = $17 + $6 = $23

Total full cost of the two books = $17 + $8 = $25

Amount of discount = $25 - $23 = $2

% reduction = [tex] \frac{2}{25} \times100\%=8\%[/tex]

Therefore, the percent of the total cost of the two books reduced during the sale is 8%

8% First, determine what book the discount is applied to. That will be the lower priced book, so the customer saves 25% of the cost of $8, giving 25% * $8 = 0.25 * $8 = $2 So there's a total savings of $2. Now determine what the total price of purchasing both books without the discount. That would be $17 + $8 = $25 And finally, determine what percent of $25 that $2 is, so $2 / $25 = 0.08 = 8%

Line g bisects line segment BC at Point H. BH = 4x and HC = 24. Find BC.

Answers

Answer: The last choice is correct
The function is a parabola U-shaped up... so it's vertex y-value is the lowest y-value of the function.
The inverse would just be the switching of the domain and range

Answer:

The length of BC is 48 units.

Step-by-step explanation:

Given information: Line g bisects line segment BC at Point H. BH = 4x and HC = 24.

It is given that line g bisects line segment BC at Point H. It means point H divides the line BC in two equal parts BH and HC.

[tex]BH=HC[/tex]

[tex]4x=24[/tex]

Divide both sides by 4.

[tex]x=6[/tex]

The value of x is 6.

[tex]BH=4x=6\times 4=24[/tex]

The length of BC is

[tex]BC=BH+HC[/tex] (Segment addition property)

[tex]BC=24+24=48[/tex]

Therefore the length of BC is 48 units.

5x+6y=3x+2 in standard form

Answers

5x + 6y = 3x + 2
5x - 3x + 6y = 2
~~~~~~~~~
2x + 6y = 2

You ride your bicycle at a rate of 10 mi/h. the distance d (in miles) that you ride is given by the function d=10t where t is the time in hours.

Answers

I think it is 1 hour

The function d = 10t signifies that you cover 10 miles of distance per hour.

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

You ride your bicycle at a rate of 10 mi/h. the distance d (in miles) that you ride is given by the function d=10t.

We have the distance [d] as the function of time as -

d = 10t

The given equation id d = 10t. The slope of the line is 10. This means that you cover 10 miles of distance in 1 hour. The graph representing the function is plotted.

Therefore, the function signifies that you cover 10 miles of distance per hour.

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Which one of the following is a perfect square A: 100, B:13, C:127, or D:102

Answers

A: 100 because a perfect square is just a number squared and 10 squared is 100 :)

Which of the following is a perfect square?
A. 100

-3(y+4)=21
solve for y
show all work please , thank u

Answers

expand the brackets first
-3y-12=21
add 12
-3y=33
divide by -3
y= -11

Distribute negative 3 to y and 4. After distributing you should have -3y+-12=21. 21 plus 12 equals 33. 33 divides by negative 3 equals negative 11.

TheValue of a stock begins at $0.05/and increase by 0.01 each month write an equation representing the value of the stock v in any months m

Answers

Because you start with $0.05, you're going to add that to whatever 0.01 is equal to after the amount of months

the equation I got was: v=0.05+(0.01m)

The linear equation can be represented as a straight line on a graph. The equation for the given case is v = 0.05 + 0.01m.

What is a Linear equation?

A linear equation is a equation that has degree as one.

To find the solution of n unknown quantities n number of equations with n number of variables are required.

Given that,

The value of stock at the beginning is $0.05,

And, its rate of increase for each month is 0.01.

Suppose the value of stock be v and the month be m,

Then, the increment in its value for any month m is $0.01m.

Now, the equation for the value of stock v at any month m can be written by summing its initial value to its increment value obtained for each month as,

v = 0.05 + 0.01m.

Hence, the equation representing the value of the stock v in any months m is given as v = 0.05 + 0.01m.

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460=50+12m what does m stand for?

Answers

50 + 12m = 460
Subtract 50 from both sides
12m = 410
Divide 12 from both sides to isolate m
m = 34 1/6

This equation should of be written as 460=12m+50, not 460=50+12m, but either way, 12 is the amount of something that being multiply by, or the slope, 50 is the y-intercept, and m is the thing that I mentioned earlier.

Which line is perpendicular to 5x + 4y = 8?
A) 4y = –5x + 4
B) 5y = 4x + 5
C)5y = –4x –15
D)4y = 5x + 12

Answers

It would be C) 5y = -4x -15

The formula for the area of a triangle is A = bh, where b is the length of the base and h is the height. The equation solved for h is h = .

Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.

3 units
5 units
8 units
9 units

Answers

a=bxh
h=a/b
h=30/12
h=2.5

The correct answer is 5 units

The mass of a proton is approximately 1.67 x 10−24, and the mass of an electron is approximately 9.11 x 10−28. Find the approximate ratio of the mass of the proton to the mass of the electron.

Answers

1.67x[10^(-20)] 1.67x[10^(-24+28)]
--------------------- = -------------------------- =
9.11x[10^(-28)] 9.11

.183315(10^4)=1833.15

The proton mass is about 1833 times an electron mass

Hope this helps!

what would is be in fraction form 1/1833 or 1833/1

How do you solve this 2 step equation: 8+b/-4=5

Answers

I'm going to rewrite the equation assuming this is the correct form:
[tex]8 - \frac{b}{4} = 5 \newline -8 + 8 - \frac{b}{4} = 5 - 8 \newline (-4)\cdot -\frac{b}{4} = -3 \cdot (-4) \newline b = -12[/tex]

Select a counter-example that makes the conclusion false.
You select three marbles from a bag and each of them is black.
Conclusion: All the marbles in the bag are black.

Counterexample:

Answers

A counter-example could be

There are more than 3 marbles in the bag, and the other ones are red.

Hope this helps!

A counterexample showing the conclusion 'All the marbles in the bag are black' as false.

A counterexample is a scenario where the premises are true but the conclusion is false, demonstrating the invalidity of an argument. In this case, to prove invalidity, a counterexample could be a situation where there is at least one marble in the bag that is not black. For instance, if there are three black marbles and one red marble inside the bag, the selection of three black marbles is still possible, but the conclusion that all marbles are black is false.

If the perimeter of the rectangle is 28 cm, find the value(s) for x.

Answers

x will always = 1 no matter what

Write an example of a linear equation with one variable and infinitely many solutions.

Answers

Infinitely many solutions means u have coincident lines...the same line

3(x + 5) = 3x + 15...this produces infinitely many solutions because it is the same line.

4x + 3 = 2x + 2x + 3....infinitely many solutions

5x - 1 = 10x - 5x - 1....infinitely many solutions

I gave u a few examples :)

Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Two times a number increased by 5 is 15. a. 2n(5) = 15 n = 1.5 c. 2n + 5 = 15 n = 20 b. 2n + 5=15 n = 5 d. n + 5 = 15 n = 10 Please select the best answer from the choices provided A B C D

Answers

2n+5=15
n=5
Looks like B

The sum of two consecutive integers is 59. Write an equation that models this situation and find the values of the two integers.

A) n + 2n = 59; n = 19; 2n = 38

B) n + n + 1 = 59; n = 29; n + 1 = 28

C) n + n + 1 = 59; n = 30; n + 1 = 31

D) n + n + 1 = 59; n = 29; n + 1 = 30

Please explain your answer! : )

Answers

The equation will be:

n + (n + 1) = 59
n + n + 1 = 59

Solving:

2n + 1 = 59
-1 -1
2n = 58
n = 29
n + 1 = 30

Hope this helps!

are these points correct??

Answers

Yes, I believe the points are indeed correct.

I think R1 (5;-1) S1 (2;-4) T1 (-2;-4) U1 (0;-1)

If the interior angle of a polygon is 170 how many sides does it have

Answers

if interior angle is 170, subtract 170 from 180 to find exterior angle:

180-170 = 10 = exterior angle

the sum of exterior angles is 360 so divide by exterior angle to find sides:

360 /10 = 36 sides

Consider the graph of the linear function h(x) = –x + 5. Which could you change to move the graph down 3 units?

Answers

the +5 because that's the y value on the graph

The +5 is the Y value

How many words of length over alphabet s contain exactly two distinct letters?

Answers

The english alphabet contains 2121 consonants and 55 vowels. How many strings of 66 lowercase letters of the English alphabet contain

a) exactly 1 vowel
b) exactly 2 vowels
c) at least one vowel
d) at least two vowels

Other Questions

PLS HELP!!!A copy center offers its customers two different pricing plans for black and white photocopies of 8.5 in. by 11 in. pages. Customers can either pay $0.08 per page or pay $7.50 for a discount card that lowers the cost to $0.05 per page. Write and solve an equation to find the number of photocopies for which the cost of each plan is the same..08c = .05c + 7.50; c = 250.05c = .08c + 7.50; c = 22.5.08c = .05c 7.50; c = 2507.50 = .08c + .05c; c = 58 In the late 1800s, meat and grain were processed in Chicago and sent eastward by _____. Almost half of Russia's land is ____-Forest-Tundra-Mountains-Steppes a. bogota b. caracas c. buenos aires d. montevideo why dis the anasazi abandon their major pueblosA. the houses were too smallB. the houses were too difficult to keep cleanC. mounds were easier to buildD. severe droughts hit If your car travels 290 miles and uses 8.2 gallons, how many miles per gallon did you get? (round your answer to three decimal places.) Which of the following might be an example of economic dominance, which Europe, the United States, and Japan often wielded over other regions?A. a treaty signed to form a military allianceB. a puppet government that was supported by foreign rulersC. a military invasion that was implemented to put down revolutionary factionsD. a commercial firm that exerted political and social power in colonized regions What did Europeans hope to gain from exploring a new world what is the role of rRNA during translation What is the relationship between the sine and cosine of complementary angles in a right triangle? Please give an example to support your answer. How do you find the quadratic equation of a parabola with the vertex and x intercept? is that ok?? i just want to make sure, thanks Becky fenton has 65/130/75 automobile insurance coverage. if two other people are awarded $110,000 each for injuries in an auto accident in which becky was judged at fault, how much of this judgment would the insurance cover? What is the boiling point of oxygen Identify the expression that is equivalent by distributive property of5(2x+3)A 10x +3B 10x + 5C 10x +15 Sally has 42 coins, all dimes and nickels, that have a total value of $3.00. How many nickels does she have? What does winston decide are the only things that matter? if confession would not be betrayal, what would be? what would this betrayal prove? Egyptian trade extended up and down the nile, including with the kush at the southern end of the river. Egypt also traded heavily in which region Describe how Iphone 8 can be used to help businesses NEED TO KNOW!!!!! San rotated parallelogram ABCD 90 clockwise around the origin. If angle A is 130 and angle B is 50, what is the degree measurement of angle AA: 80 degreesB: 130 degrees C: 50 degrees D: 180 degrees Steam Workshop Downloader