the base of a pyramid has the same area as the base of a cylinder, and the cylinder is twice the height of the pyramid. What is the ratio of the volume of the pyramid to the volume of the cylinder?

Answers

Answer 1
Final answer:

The ratio of the volume of a pyramid with base area A and height h to the volume of a cylinder with the same base area and twice the height is 1:6.

Explanation:

The question asks about finding the ratio of the volume of a pyramid to the volume of a cylinder when they have equal base areas and the height of the cylinder is double that of the pyramid. We can use the standard volume formulas for both shapes. The volume of a pyramid is given by Vpyramid = (1/3)Ahpyramid, where A is the area of the base and hpyramid is the height of the pyramid. For the cylinder, the volume is Vcylinder = Ahcylinder, with hcylinder being the height of the cylinder. Since the cylinder's height is twice that of the pyramid, we can write hcylinder = 2hpyramid. Plugging in the values and simplifying, we get the ratio of volumes as 1:6.

Answer 2

The volume ratio of the pyramid to the cylinder, with equal base areas and the cylinder being twice as high, is 1:6.

What is the ratio of their volume?

Let A be the area of the base of both the pyramid and the cylinder, [tex]h_p[/tex] be the height of the pyramid, and [tex]h_c[/tex] be the height of the cylinder.

The volume (V) of a pyramid is given by [tex]V_p = \frac{1}{3}A h_p[/tex].

The volume (V) of a cylinder is given by [tex]V_c = A h_c[/tex].

Given that [tex]h_c[/tex] is twice [tex]h_p[/tex], we can express [tex]h_c = 2h_p[/tex].

Find the ratio:

Ratio = [tex]\frac{V_p}{V_c} = \frac{\frac{1}{3}A h_p}{Ah_c}[/tex]

Substitute [tex]h_c = 2h_p[/tex]:

Ratio = [tex]\frac{\frac{1}{3}A h_p}{A(2h_p)} = \frac{\frac{1}{3}h_p}{2h_p}[/tex]

Cancel out [tex]h_p[/tex]:

Ratio = 1/6

So, the ratio of the volume of the pyramid to the volume of the cylinder is 1/6.


Related Questions

which of the following is a tip for taking the aspire reading test

Answers

A tip for taking the aspire reading test is to read the entire given text before you answer any of the questions. Hope this helps and good luck on the test!

Answer: refer to the passage when answering the question

Explanation: apex

which of the following is a tip for taking the aspire reading test

Answers

1. Pace Yourself
2. Familiarize Yourself with Writing Styles
3. Consider the Context
4. Be Careful
Take notes during the test that might be important later. These might end up helping when you answer the questions.

If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?
[Hint: Place your coordinates in the blank with no parentheses and a space after the comma in the form: x, y]

Answers

the answer is 1, 1 because it returns back to its first position

Answer: coordinates x = 1, y = 1.


Explanation:


You can deduce the answer analytically by using these mathematical rules:


1. First transformation. Reflection over the y-axis means that the image will keep the same y-coordinate and negate the x-coordinate (the image will end in the left quadrant at the same height):

rule (x,y) → (- x, y)

          A(1,1) → A'(-1,1)

          B(2,2) → B'(-2,2)

          C(4,2) → C'(-4,2)

          D(5,1) → D'(-5,1)


2. Second transformation. The reflection over the x-axis tansforms the image by keeping the same x-coordinate and negating the y-coordinate, the image will end in the fhird quadrant right below the previous image:

rule (x,y) → (x, - y)

          A'(-1,1) → A''(-1,-1)

          B'(-2,2) → B''(-2,-2)

          C'(-4,2) → C''(-4,-2)

          D'(-5,1) → D''(-5,-1)


3. Third transformation. The rotation 180° (either counterclockwise or clockwise) negates both coordinates x and y:

rule (x,y) → (- x, - y)

          A''(-1,-1) → A'''(1,1) ← this is the answer

          B''(-2,-2) → B'''(2,2)

          C''(-4,-2) → C'''(4,2)

          D''(-5,-1) → D'''(5,1)

As you see the final images of every point correspond to same original point.


Why is Pluto now called a dwarf planet?

Answers

Answer:

In 2003, astronomers discovered Eris.

The discovery of Eris caused astronomers to talk about the defining characteristics of a planet.

Because Pluto has not cleared its orbit, it is not considered to be a planet.

Pluto, Eris, and other objects like them are now classified as dwarf planets.

Pluto is called a dwarf planet because of its size and the fact that it's located within a zone (transneptunian region) of other celestial objects with its size

Why is Pluto called a dwarf planet?

The reason why Pluto is classified and called a dwarf planet is simply because of its size and the fact that it's located within a zone (transneptunian region) of other celestial objects with its size.

Additionally, Pluto does not have a cleared orbit and as such, it is classified and called a dwarf planet alongside other celestial objects such as:

ErisCeresMakemakeHaumea

Read more on planets here: brainly.com/question/1286910

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How many points do football teams score in the super bowl? Here are the total numbers of points scored by both teams in each of the the first 48 super bowl games. Display these data in a stem-leaf plot

Answers

24. The stem-and-leaf plot for Super Bowl points shows the distribution of total points scored by both teams in the first 48 games, ranging from 21 to 75.

25. The stem-and-leaf plot for Super Bowl wins illustrates the winning margins for the first 48 games, ranging from 1 to 45 points. It provides a clear view of the distribution of winning differences.

24. Super Bowl Points - Stem-and-Leaf Plot:

Here are the total points scored by both teams in each of the first 48 Super Bowl games, displayed in a stem-and-leaf plot:

Stem | Leaf

------------

 2  | 1 2 2 7

 3  | 0 1 1 6 6 7 7 8 9 9

 4  | 1 3 4 4 5 6 7 7

 5  | 0 1 3 4 5 6 6 7 9

 6  | 1 5 5 6 9

 7  | 5 5

In this plot, the stem represents the tens digit, and the leaf represents the ones digit. For example, the entry "36" in the stem-and-leaf plot corresponds to the actual value of 36 points.

25. Super Bowl Wins - Stem-and-Leaf Plot:

Here are the winning margins for the first 48 Super Bowl games, displayed in a stem-and-leaf plot:

Stem | Leaf

------------

 0  | 1 3 3 4 4 4 4 4 5 6 7 7 7 9

 1  | 0 0 0 1 2 3 4 5 6 7 7 9

 2  | 2 2 3 7 9

 3  | 2 3 3 4 5 5 5 6 7

 4  | 3 4 4 5 5 5

In this plot, the stem represents the tens digit, and the leaf represents the ones digit. For example, the entry "23" in the stem-and-leaf plot corresponds to the actual winning margin of 23 points.

Your engine might be flooded if you smell what while driving

Answers

I think it's Carbon monoxide

Overfilling your tank increases the risk of liquid gas covering the vapour intake hole and entering the charcoal canister. The check engine light will illuminate as a result of this damage to the canister and possibly other components of the system, which might cost hundreds of dollars to fix.

What engine might be flooded if you smell while driving?

A flooded engine may have a gas-like odour that you can detect. Colour of the emission: Darker smoke may also indicate that your engine is flooded. Trouble starting: If the engine has too much fuel, your car may have trouble starting.

Furthermore, too much gas covers the spark plugs, preventing them from producing the spark required for combustion. If you try to start your car by pressing the gas pedal too frequently, engine flooding frequently results.

Therefore, Your engine might be flooded if you smell what while driving because it is carbon monoxide gas.

Learn more about driving here:

https://brainly.com/question/16442586

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