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
9,682 in.3
9,682 inches cubed
16,747 in.3
16,747 inches cubed
19,363 in.3
19,363 inches cubed
7,065 in.3
To calculate the volume of Kairay's sculpture, we need to find the volume of both the larger hemisphere with a radius of 20 inches and the smaller hemisphere with a radius of 15 inches, then subtract the volume of the smaller hemisphere from the larger one. The formula for the volume of a sphere (and thus a hemisphere, which is half a sphere) is:
Volume of a sphere = (4/3)πr³
Since we only need half of that volume for a hemisphere:
Volume of a hemisphere = (1/2)(4/3)πr³
= (2/3)πr³
We'll calculate each hemisphere's volume separately and then subtract the smaller from the larger:
Volume of the larger hemisphere (r = 20 inches):
V_large = (2/3)π(20 inches)³
≈ (2/3)(3.14)(20 inches)³
≈ (2/3)(3.14)(8000 in³)
≈ (2/3)(25120 in³)
≈ 16746.67 in³
Volume of the smaller hemisphere (r = 15 inches):
V_small = (2/3)π(15 inches)³
≈ (2/3)(3.14)(15 inches)³
≈ (2/3)(3.14)(3375 in³)
≈ (2/3)(10593.75 in³)
≈ 7062.5 in³
Now we subtract the volume of the smaller hemisphere from the larger one to find the volume of the sculpture:
Volume of the sculpture = V_large - V_small
≈ 16746.67 in³ - 7062.5 in³
≈ 9684.17 in³
Rounded to the nearest whole number, the volume of the sculpture is approximately 9684 in³.
Thus, the closest answer is:
9,682 in.3 or 9,682 inches cubed