Finding the volume of a cone, given the volume of a similar cone.

[juliarose]

Cone A has 3 times the radius and 3 times the height of Cone B. The volume of Cone B is 25pi cubic feet. What is the volume of Cone A?

 

[mmm4444bot]

Hello. Did you read the forum's submission guidelines (READ BEFORE POSTING)?

Do you know the volume formula for a cone?

What have you tried? Where did you get stuck?

?

 

[Otis]

Hi. Here are some steps:

If you don't know the formula for the volume of a cone, then please look it up. (Use your textbook's index, or google it.)

Let r = radius of cone B

Let h = height of cone B

Let 25∙Pi = volume of cone B

Use the expressions above in the volume formula, to write an equation for cone B.

Now, what expression can we write for the radius of cone A?

What expression can we write for the height of cone A?

Let V = volume of cone A

Again, use the volume formula, to write an equation for cone A.

Next, use algebra to rearrange both equations so that the right-hand sides looks like this:

Pi∙r^2∙h

Once you've done that, you can see that the two left-hand sides are equal. So, set them equal to one another (to form a new equation), and then solve it for V.

If you'd like more help, please follow the guidelines and show your work and/or ask specific questions. Cheers

\(\;\)

 

[MarkFL]

Another approach: If the linear measures of a solid (solid 1) are \(a\) times that of another similar solid (solid 2), then the volume of solid 1 will be \(a^3\) times as great as that of solid 2.