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
19,363 in.3
19,363 inches cubed
9,682 in.3
9,682 inches cubed
16,747 in.3
To calculate the volume of the sculpture, we first need to find the volume of the larger hemisphere and then subtract the volume of the smaller hemisphere.
The volume of a hemisphere can be calculated using the formula V = (4/3)Ď€r^3, where r is the radius.
For the larger hemisphere with a radius of 20 inches:
V1 = (4/3)(3.14)(20)^3 = 33,493.33 in.3
For the smaller hemisphere with a radius of 15 inches:
V2 = (4/3)(3.14)(15)^3 = 14,137.33 in.3
To find the volume of the sculpture, we subtract V2 from V1:
Volume = V1 - V2 = 33,493.33 - 14,137.33 = 19,356 in.3
Rounding to the nearest whole number, we get 19,363 in.3.
Therefore, the correct answer is:
19,363 inches cubed