Question

The volume of a hemisphere is 144 pi. Find the radius and total surface area.

Answer 1

Formula of the Volume of a hemisphere:
V =
`(2)/(3)`
`\pi`r³
144
`\pi` =
`(2)/(3)`
`\pi`r³
Multiply by 3 to cancel fraction in the right side
144
`\pi` × 3 = 2
`\pi` r³
432
`\pi` = 2
`\pi`r³
Divide by 2
`\pi` on either sides to isolate r³

`(432 \pi )/(2 \pi )` =
`(2 \pi )/(2 \pi )`r³
2
`\pi` and
`2 \pi` cancel out
216 = r³
Take cube root to find the radius

`\sqrt[3]{216}` =
`\sqrt[3]{r^3}`
6 = r
Radius is 6 units

The formula of the surface area of a hemisphere is:
S.A = 2
`\pi`r² +
`\pi`r²
=
`2\pi`(6)² +
`\pi`(6)²
=2
`\pi` × 36 + 36
`\pi`
= 72
`\pi` + 36
`\pi`
= 108
`\pi` units² (in terms of
`\pi`)
≈ 339.12 units²

Surface area = 108
`\pi` units