Question

Chef Pierre can do something unique. Using a secret process, he can bake a nearly perfectly spherical pie consisting of a vegetable filling inside a thick crust. The radius of the whole pie is 12 cm, and the radius of the filling is 8 cm. What is the volume of the crust alone, to the nearest unit? Use p = 3.14.

Answer 1

The volume of Chef Pierre's pie crust is calculated by subtracting the volume of the vegetable filling from the volume of the entire pie, yielding approximately 5,091 cm³.

Step-by-step explanation:

To determine the volume of the crust of Chef Pierre's spherical pie, we need to calculate the volume of the entire pie and then subtract the volume of the vegetable filling. The formula for the volume of a sphere is V = (4/3)πr³. First, we calculate the volume of the whole pie (including crust) with a radius of 12 cm, and then the volume of the vegetable filling with a radius of 8 cm.

Volume of whole pie: Vwhole = (4/3)π(12 cm)³ = (4/3) * 3.14 * (12 cm)³ ≈ (4/3) * 3.14 * 1,728 cm³ ≈ 7,238.56 cm³

Volume of vegetable filling: Vfilling = (4/3)π(8 cm)³ = (4/3) * 3.14 * (8 cm)³ ≈ (4/3) * 3.14 * 512 cm³ ≈ 2,147.97 cm³

Subtract the volume of the filling from the volume of the whole pie to get the volume of the crust alone:

Volume of crust alone: Vcrust = Vwhole - Vfilling ≈ 7,238.56 cm³ - 2,147.97 cm³ ≈ 5,090.59 cm³

To the nearest unit, the volume of the crust is approximately 5,091 cm³.

Answer 2

Given that the crust formed is cylindrical with the height which is equal to the radius of the sphere, then the volume will be given by:
V=πr^2h
V=π*8^2*12
V=2,412.743 cm^3
We conclude that the volume of the crust is 2,412.743 cm^3