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?

A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm

Answer 1

B) 3 cm

Vsphere =
`(4)/(3)\pi r^(3) = (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; \ <=> \ (4 \pi)/(3)*3^3=(1)/(3) \pi*6^2*h_c; \ => \ h_c=3(cm)`

answer: B