a. The volume of the cylinder is 216π cm³
b. The volume of the cone is 72π cm³
c. The volume of the hemisphere is 144π cm³
a. Volume of the cylinder
The volume of the cylinder is 216π cm³
Since the hemisphere fits snugly inside the cylinder, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.
So, the volume of the cylinder V = πr²h where
- r = radius of cylinder = 6 cm and
- h = height of cylinder = radius of hemisphere = 6 cm
So, V = πr²h
= πr² × r
= πr³
= π(6 cm)³
= 216π cm³
So, the volume of the cylinder is 216π cm³
b. Volume of the cone
The volume of the cone is 72π cm³
Since the cone fits snugly inside the same hemisphere, the radius and height of the cone equals the radius of the hemisphere.
So, the volume of the cone V' = πr²h/3 where
- r = radius of cone = 6 cm and
- h = height of cone = radius of hemisphere = 6 cm
So, V' = πr²h/3
= πr² × r/3
= πr³/3
= π(6 cm)³/3
= 216π/3 cm³
= 72π cm³
So, the volume of the cone is 72π cm³
c. Volume of hemisphere
The volume of the hemisphere is 144π cm³
Since the volume of hemisphere, V" equals the averages of the volume of the cylinder, V and volume of the cone, V'
So, V" = (V + V')/2
V" = (216π cm³ + 72π cm³)/2
V" = 288π cm³/2
V" = 144π cm³
So, the volume of the hemisphere is 144π cm³
Learn more about volume here:
https://brainly.com/question/25248189
