Question

If a sphere has a diameter of 12 units, what is the volume of half of the sphere?

Answer 1

see explanation

Explanation:

The volume (V) of a sphere is

V =
`(4)/(3)`πr³ ( r is the radius )

here diameter = 12, hence radius = 6

The volume of half of the sphere is

V =
`(1)/(2)` ×
`(4)/(3)`πr³

=
`(2)/(3)`πr³

=
`(2)/(3)`π × 6³

=
`(2)/(3)`π × 216 ← cancel 3 and 216

= 2π × 72

= 144π units³ ← exact value

≈ 452.39 units³ ( to 2 dec. places )