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
16,747 in.3
16,747 inches cubed
9,682 in.3
9,682 inches cubed
7,065 in.3
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 can be calculated using the formula V = (2/3) * pi * r^3.
First, let's calculate the volume of the larger hemisphere with a radius of 20 inches:
V1 = (2/3) * 3.14 * (20^3) = 33,493.33 in^3
Next, let's calculate the volume of the smaller hemisphere with a radius of 15 inches:
V2 = (2/3) * 3.14 * (15^3) = 14,137.50 in^3
Finally, subtract V2 from V1 to find the volume of the sculpture:
Volume of sculpture = V1 - V2 = 33,493.33 - 14,137.50 = 19,355.83 in^3
Rounded to the nearest whole number, the volume of the sculpture is 19,356 in^3.
Therefore, the correct answer is:
19,363 in.3