Question

Kairay created a sculpture by forming a hemisphere with a radius of 20 inches and then removing a hemisphere with a radius of 15 inches from it. Calculate the volume of his sculpture. Use 3.14 as an approximation for pi. Round your answer to the nearest whole number.(1 point) Responses 16,747 in.3 16,747 inches cubed 19,363 in.3 19,363 inches cubed 7,065 in.3 7,065 inches cubed 9,682 in.3

Answer 1

To calculate the volume of the sculpture, we need to find the volume of the larger hemisphere and subtract the volume of the smaller hemisphere that was removed.

The volume of a hemisphere is given by (2/3) * π * r^3, where r is the radius.

First, let's calculate the volume of the larger hemisphere (with radius 20 inches):

V_large = (2/3) * π * r^3
V_large = (2/3) * 3.14 * 20^3
V_large = (2/3) * 3.14 * 8000
V_large = (2/3) * 3.14 * 8 * 1000
V_large = (2/3) * 25.12 * 1000
V_large = 16.74666667 * 1000
V_large = 16746.66667 cubic inches

Now, let's calculate the volume of the smaller hemisphere (with radius 15 inches):

V_small = (2/3) * π * r^3
V_small = (2/3) * 3.14 * 15^3
V_small = (2/3) * 3.14 * 3375
V_small = (2/3) * 3.14 * 3.375 * 1000
V_small = (2/3) * 10.5975 * 1000
V_small = 7.065 * 1000
V_small = 7065 cubic inches

Now let's subtract the volume of the smaller hemisphere from the volume of the larger hemisphere to get the volume of the sculpture:

V_sculpture = V_large - V_small
V_sculpture = 16746.66667 - 7065
V_sculpture = 9681.66667 cubic inches

Rounding to the nearest whole number, the volume of the sculpture is 9682 cubic inches.

Therefore, the closest answer given is:
9,682 in.3 or 9,682 inches cubed.