airay 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
7,065 in.3
7,065 inches cubed
16,747 in.3
16,747 inches cubed
19,363 in.3
19,363 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 volume of a hemisphere can be calculated using the formula: V = (2/3)πr³.
The volume of the larger hemisphere with a radius of 20 inches is:
V1 = (2/3)π(20)^3
V1 ≈ (2/3)(3.14)(20^3)
V1 ≈ (2/3)(3.14)(8000)
V1 ≈ 33546.67
The volume of the smaller hemisphere with a radius of 15 inches is:
V2 = (2/3)π(15)^3
V2 ≈ (2/3)(3.14)(15^3)
V2 ≈ (2/3)(3.14)(3375)
V2 ≈ 7065.00
The volume of the sculpture is the difference between the two volumes:
V = V1 - V2
V ≈ 33546.67 - 7065.00
V ≈ 26481.67
Rounding to the nearest whole number, the volume of the sculpture is approximately 26,482 in.³.
Therefore, the correct answer is not listed in the given responses.