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
7,065 in.3
7,065 inches cubed
9,682 in.3
9,682 inches cubed
19,363 in.3
To calculate the volume of the sculpture, we first need to find the volume of the larger hemisphere and then subtract the volume of the smaller hemisphere.
The volume of a hemisphere is given by the formula: (2/3) * pi * r^3.
For the larger hemisphere with a radius of 20 inches, the volume is:
V1 = (2/3) * 3.14 * (20^3)
= (2/3) * 3.14 * 8000
= 16,747 inches cubed (rounded to the nearest whole number)
For the smaller hemisphere with a radius of 15 inches, the volume is:
V2 = (2/3) * 3.14 * (15^3)
= (2/3) * 3.14 * 3375
= 7,065 inches cubed (rounded to the nearest whole number)
Therefore, the volume of the sculpture is V1 - V2 = 16,747 - 7,065 = 9,682 inches cubed.