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
9,682 in.3
9,682 inches cubed
16,747 in.3
16,747 inches cubed
To calculate the volume of the sculpture, we need to find the difference in volume between the larger hemisphere (radius of 20 inches) and the smaller hemisphere (radius of 15 inches).
The formula for the volume of a hemisphere is:
V = (2/3)πr^3
For the larger hemisphere:
V1 = (2/3)π(20)^3
For the smaller hemisphere:
V2 = (2/3)π(15)^3
To find the volume of the sculpture, we need to subtract V2 from V1:
Volume of sculpture = V1 - V2
Calculating the values:
V1 = (2/3)π(20)^3
V1 = (2/3)(3.14)(8000)
V1 = 33,493.33 in^3
V2 = (2/3)π(15)^3
V2 = (2/3)(3.14)(3375)
V2 = 11,305 in^3
Volume of sculpture = V1 - V2
Volume of sculpture = 33,493.33 - 11,305
Volume of sculpture ≈ 22,188.33
Rounding to the nearest whole number:
Volume of sculpture ≈ 22,188 in^3
Therefore, the volume of the sculpture is 22,188 inches cubed.