Question

Please help!

Suppose that a sphere with radius 5a has the same volume as a cone of radius 3a. What is the height of the cone? Give your answer in terms of a. Use the formulas of A and B for the volumes of a sphere and cone respectively.

Formula A: http://i1255.photobucket.com/albums/hh639/zigzagoon20001/FormulaA.jpg

Formula B: http://i1255.photobucket.com/albums/hh639/zigzagoon20001/FormulaB.jpg

A. 9/500a

B. 500/9a^2

C. 9/500a^2

D. 500/9a

A, B, C, or D? Please explain (:

Answer 1

well since the volume is the same for each shape, set the two equal to each other, and plug in your radius and solve for h

so ... (4/3)pi(5a)^3 = (1/3)pi(3a)^2(h)