Question

A coconut is a fruit that is made up of a hard outer shell that is spherical. Inside, there is a thick layer of coconut meat that forms another spherical shell around the coconut milk. If the diameter of an entire coconut is 5 inches, and the coconut meat is 1 inch thick, then there is room for approximately _[blank]_ in3 of coconut milk. What number correctly fills in the blank in the previous sentence? Hint: Find the radius of the inside sphere and use that to calculate the volume. Use 3.14 for π and round your answer to the nearest hundredth, if necessary, like this: 42.53

Answer 1

The volume of coconut milk that can fit inside the coconut, calculated using the volume of a sphere formula, is approximately 13.15 in³.

Step-by-step explanation:

To solve this problem, we'll calculate the volume of the spherical space where the coconut milk is, using the formula for the volume of a sphere. The diameter of the entire coconut is 5 inches, so the radius is half of that, which is 2.5 inches.

Since the coconut meat is 1 inch thick, we subtract that thickness from the radius of the full coconut to find the inner radius, which is 1.5 inches.

The formula for the volume of a sphere is V = 4/3πr³, where π is approximated as 3.14 and r is the radius. Plugging in our inner radius:

V = 4/3π(1.5 inches)³

V = 4/3π(3.375 inches³)

V = 4.188π inches³

V ≈ 4.188 × 3.14 inches³

V ≈ 13.15032 inches³

When rounded to the nearest hundredth, the volume of coconut milk that fits inside the coconut is approximately 13.15 in³.

Answer 2

Volume = 33.41in³

Step-by-step explanation:

Since the coconut has a shape of a sphere,

Volume of a sphere(v) = 4/3 πr³

V = volume

π = 3.14

r = radius of the sphere.

The diametere of the entire coconut = 5inches

The diameter of the coconut meat = 1 inches

Diameter of space remaining = 5 - 1 = 4 inches

Radius = diameter / 2

Radius = 4 / 2 = 2 inches

Volume = 4/3 × πr³

Volume = 4/3 × 3.14 × 2³

Volume = 1.33 × 3.14 × 8

Volume = 33.4096in³

Volume of milk that can fill the coconut is approximately 33.41in³