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
7,065 in.3
7,065 inches cubed
16,747 in.3
16,747 inches cubed
9,682 in.3
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.
The formula for the volume of a hemisphere is (2/3)πr³.
For the larger hemisphere with a radius of 20 inches:
Volume = (2/3)π(20)^3
Volume = (2/3)π(8000)
Volume = (16000/3)π
Volume ≈ 16747 in.3
For the smaller hemisphere with a radius of 15 inches:
Volume = (2/3)π(15)^3
Volume = (2/3)π(3375)
Volume = (2250/3)π
Volume ≈ 7065 in.3
Finally, we subtract the volume of the smaller hemisphere from the volume of the larger hemisphere:
16747 - 7065 = 9682 in.3
Therefore, the correct answer is 9,682 in.3.