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
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.
Solving for h gives
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*(10)^2*(1.528) = 160 cm^3
- Algebra - Reiny, Monday, February 18, 2013 at 12:35am
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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