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 V=4/3pier^3 and V=1/3pier^2h for the volumes of a sphere and cone respectively.
A. 9/500a

B. 500/9 a2

C. 9/500 a2

D. 500/9a

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 V=4/3pier^3  and V=1/3pier^2h for the volumes of a sphere and cone respectively. 
 A. 9/500a  
 
 B. 500/9 a2  
 
 C. 9/500  a2  
 
 D. 500/9a

ganpat · Answer

V sp = V cone 

4/3 pi r cube = 1/3 pi r square  * h 

4 * 5a cube = 3a square * h 

h = 4 * 125 a / 9 = 500a/ 9... option D...

anonymous · Answer

so the answer is d