Question

A grapefruit has a peel that is 1cm thick and a total diameter of 12cm. What percentage of volume of the grapefruit is the peel?

Answer 1

Answer:

0.3056 or 30.56%

Step-by-step explanation:

The volume of the grapefruit with the peel is:

$V_p=\frac{4 \pi (d/2)^2}{3}\\V_p=\frac{4 \pi (12/2)^2}{3}\\V_p=48 \pi$

When removing the peel, the grapefruit diameter becomes 10 cm (take out 1 cm of peel from each side). The volume of the grapefruit without the peel is:

$V_n=\frac{4 \pi (d/2)^2}{3}\\V_n=\frac{4 \pi (10/2)^2}{3}\\V_n=33.333 \pi$

The percentage of the volume correspondent to the peel is given by the difference between both volumes, divided by the total volume:

$\%P = \frac{48\pi - 33.333\pi}{48\pi}\\ \%P =0.3056 = 30.56\%$

30.56% of volume of the grapefruit is the peel.