Answer:
810π cm³
Step-by-step explanation:
The figure is a hemisphere cone.
We can calculate the volumes of the two portions separately.
(a) Volume of the cone
Diameter of hemisphere = 18 cm
Radius of hemisphere = 9 cm
Height of cone + hemisphere = 21 cm
h + 9 = 21 Subtract 9 from each side
h = 12 cm
The formula for the volume of a cone is
V₁ = ⅓πr²h
V₁ = ⅓π × 9² × 12
= ⅓π × 81 × 12
= 324π cm³
(b) Volume of hemisphere
The formula for the volume of a sphere is
V = ⁴/₃πr³
So, the formula for the volume of a hemisphere is
V = ⅔πr³
V₂ = ⅔π × 9³
V₂ = ⅔π × 729
= 486π cm³
(c) Volume of hemisphere cone
V = V₁ + V₂
= 324π + 486π
= 810π cm³
