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
7,065 in.3
7,065 inches cubed
9,682 in.3
9,682 inches cubed
16,747 in.3
16,747 inches cubed
19,363 in.3
To calculate the volume of the sculpture, we can use the formula for the volume of a hemisphere:
Volume of hemisphere = (2/3) * pi * r^3
First, let's calculate the volume of the larger hemisphere with a radius of 20 inches:
Volume of larger hemisphere = (2/3) * 3.14 * 20^3
= (2/3) * 3.14 * 8,000
= 33,493.33 in.3 (rounded to the nearest whole number)
Next, let's calculate the volume of the smaller hemisphere with a radius of 15 inches:
Volume of smaller hemisphere = (2/3) * 3.14 * 15^3
= (2/3) * 3.14 * 3,375
= 7,094.6 in.3 (rounded to the nearest whole number)
Finally, let's subtract the volume of the smaller hemisphere from the volume of the larger hemisphere to find the volume of the sculpture:
Volume of sculpture = Volume of larger hemisphere - Volume of smaller hemisphere
= 33,493.33 - 7,094.6
= 26,398.73 in.3 (rounded to the nearest whole number)
Therefore, the volume of Kairay's sculpture is approximately 26,398 in.3.