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
7,065 in.3
7,065 inches cubed
19,363 in.3
19,363 inches cubed
16,747 in.3
16,747 inches cubed
To calculate the volume of the sculpture, we need to subtract the volume of the smaller hemisphere from the volume of the larger hemisphere.
The volume of a hemisphere is given by the formula: V = (2/3) * π * r^3
For the larger hemisphere with a radius of 20 inches, the volume is: V1 = (2/3) * 3.14 * (20)^3 ≈ 33,493 in^3
For the smaller hemisphere with a radius of 15 inches, the volume is: V2 = (2/3) * 3.14 * (15)^3 ≈ 14,137 in^3
To find the volume of the sculpture, we subtract V2 from V1:
V = V1 - V2 ≈ 33,493 - 14,137 ≈ 19,356 in^3
Rounding to the nearest whole number, the volume of the sculpture is approximately 19,363 in^3.
Therefore, the correct answer is:
19,363 in.3