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
Attached Figure / Diagram
A
36\(\pi\)cm 3
B
54\(\pi\)cm 2
C
18\(\pi\)cm 2
D
108\(\pi\)cm 2
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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 = \(\frac{4 \pi r^3}{6} = \frac{2 \pi r^3}{3}\)
= \(\frac{2 \pi}{3} \times (3)^3 = 18\pi cm^3\)
vol. of solid = 18\(\pi\) + 18\(\pi\)
= 36\(\pi\)cm3
Source: Myschool Past Questions Archive (Record #32879)