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
19,363 in.3
19,363 inches cubed
16,747 in.3
16,747 inches cubed
7,065 in.3
7,065 inches cubed
9,682 in.3
To calculate the volume of the sculpture, we first need to calculate 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 V = (2/3)πr^3, where r is the radius.
For the larger hemisphere:
V1 = (2/3)π(20)^3
V1 ≈ 33510.6667 in.3
For the smaller hemisphere:
V2 = (2/3)π(15)^3
V2 ≈ 14137.5 in.3
Now, we subtract the volume of the smaller hemisphere from the volume of the larger hemisphere:
V1 - V2 ≈ 33510.6667 - 14137.5
≈ 19373.1667 in.3
Rounding to the nearest whole number, the volume of the sculpture is approximately 19,373 in.3.
Therefore, the correct answer is:
19,363 inches cubed.