Question

The circumference of a grapefruit is 4π cm. Find the surface area of the grapefruit. Express your answer in terms of π.

a) 16 pie cm2
b) 32 pie cm2
c) 64 pie cm2
d) 72 pie cm2

Answer 1

Option (a) is correct.

The surface area of sphere is
`16\pi` cm²

Explanation:

Given : The circumference of a grapefruit is 4π cm.

We have to find the surface area of the grape fruit.

Since, Given the circumference of grape = 4π cm.

and grape is shape of sphere.

So circumference of sphere =
`2\pi r`

Thus,

`4\pi=2\pi r`

Simplify for r , we get,

`2=r`

Thus, The surface area of sphere =
`4\pi r^2`

Substitute, r = 2 cm

We have,

The surface area of sphere =
`4\pi (2)^2`

Simplify, we get,

Thus, The surface area of sphere is
`16\pi` cm².

Answer 2

We find radius first:
C = 2 * pie * r
r = C/(2 pie) = 4 pie cm / (2 pie) = 2 cm
Now we find surface area: A = 4r˛ = 4 (2)^2 = 16 pie cm2
Hence the surface area of the grapefruit fruit is 16 pie cm2.