Question

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

Volume of Sphere:

V = (4/3)pi*r^3

V = (4/3)pi*(5a)^3

V = (4/3)pi*125a^3

Volume of Cone:

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

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

V = (1/3)*pi*9a^2*h

Answer 2

The two volumes are equal, so we can say


Volume of Sphere = Volume of Cone

(4/3)pi*125a^3 = (1/3)*pi*9a^2*h

Now solve for h