Question

A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?

Answer 1

B)    3 cm

Vsphere = $\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi$

Vcone =

1

3

πr2h

36π =

1

3

π(6)2h

36π = 12πh

h = 3

Thus, the height is 3 cm.

Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.

Answer 2

Try this option:

$if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)$

answer: B