In the figure, a solid consists of a hemisphere surmounted by a right circular cone, with radius 3.0cm and height 6.0cm. Find the volume of the solid
-
A.
36(pi)cm 3 -
B.
54(pi)cm 2 -
C.
18(pi)cm 2 -
D.
108(pi)cm 2
Correct Answer: Option A
Explanation
The volume of the solid = vol. of cone + vol. of hemisphere
volume of cone = (frac{1}{3} pi r^2 h)
= (frac{1 pi}{3} times (3)^2 x 6 = 18 pi cm^2)
vol. of hemisphere = (frac{4 pi r^3}{6} = frac{2 pi r^3}{3})
= (frac{2 pi}{3} times (3)^3 = 18pi cm^3)
vol. of solid = 18(pi) + 18(pi)
= 36(pi)cm3