Posted by **Cassie** on Sunday, February 17, 2013 at 11:52pm.

A cone has a radius of 15 cm and a volume of 540 cm3. Find the volume of a similar cone with a radius of 10 cm.

A. 54 cm^3

B. 240 cm^3

C. 16 cm^3

D. 360 cm^3

I think its D but by the process of elimination...don't know how to figure it out really...?

- Algebra -
**Jeff**, Monday, February 18, 2013 at 12:14am
Could Answer c be 160 cm^3 and not 16 cm^3?

- Algebra -
**Cassie**, Monday, February 18, 2013 at 12:16am
yes it is sorry.

- Algebra -
**Jeff**, Monday, February 18, 2013 at 12:28am
The answer would then be C. 160 cm^3

The Volume of a cone is given by

V=(1/3)*pi*r^2*h

We know V= 540 cm^3 and that r=15 cm and can plug into the equation to find h.

I am going to leave the units off, but you should include it in your work.

540=(1/3)*pi*(15)^2*h

Solving for h gives

h=2.292 cm

Now a similar cone will have the same ratio

h1/r1 = h2/r2

(2.292 / 15) = (h2 / 10) and solve for h2.

h2 = 1.528 cm

Throw this into the Volume of a cone

V=(1/3)*pi*r^2*h

V=(1/3)*pi*(10)^2*(1.528) = 160 cm^3

- Algebra -
**Reiny**, Monday, February 18, 2013 at 12:35am
simpler way:

the volume of 2 similar solids is proportional to the cube of their sides

V/540 = 10^3/15^3

V = 540(1000)/(3375) = 160

- Algebra -
**Cassie**, Monday, February 18, 2013 at 1:03am
Thank you both...

- Algebra -
**Monkey D. Luffy**, Wednesday, April 1, 2015 at 3:45pm
c i got 100%

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