Question

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. Please round your answer to the nearest whole number.

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to calculate the volume of the original hemisphere. The formula for the volume of a hemisphere is V = (2/3)πr^3.

Plugging in the radius of 20 inches, we get:
V1 = (2/3) * 3.14 * 20^3
V1 = (2/3) * 3.14 * 8000
V1 = 0.66667 * 25120
V1 = 16746.72

Now, we need to calculate the volume of the removed hemisphere. The formula for the volume of a hemisphere is the same, V = (2/3)πr^3.

Plugging in the radius of 15 inches, we get:
V2 = (2/3) * 3.14 * 15^3
V2 = (2/3) * 3.14 * 3375
V2 = 0.66667 * 10642.5
V2 = 7095

To find the volume of the sculpture, we subtract V2 from V1:
V = V1 - V2
V = 16746.72 - 7095
V = 9651.72

We round this to the nearest whole number:
V≈ 9652

Therefore, the volume of his sculpture is approximately 9652 cubic inches.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the error. Let's recalculate the volume of the sculpture.

The volume of the larger hemisphere (original sculpture) is:
V1 = (2/3) * π * 20^3
V1 = (2/3) * 3.14 * 8000
V1 = 16747.2 cubic inches

The volume of the smaller hemisphere (removed part) is:
V2 = (2/3) * π * 15^3
V2 = (2/3) * 3.14 * 3375
V2 = 7068.6 cubic inches

Therefore, the volume of the sculpture is:
V = V1 - V2
V = 16747.2 - 7068.6
V = 9678.6 cubic inches

Rounding to the nearest whole number, the volume of Kairay's sculpture is approximately 9679 cubic inches.

Answer 4

also wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the oversight. Let's recalculate the volume of the sculpture.

The volume of the larger hemisphere (original sculpture) with a radius of 20 inches is calculated as:

V1 = (2/3) * π * 20^3
V1 = (2/3) * 3.14 * 8000
V1 = 16755.47 cubic inches

The volume of the smaller hemisphere (removed part) with a radius of 15 inches is calculated as:

V2 = (2/3) * π * 15^3
V2 = (2/3) * 3.14 * 3375
V2 = 7069.8 cubic inches

The volume of the final sculpture after removing the smaller hemisphere from the larger one is:

V = V1 - V2
V = 16755.47 - 7069.8
V = 9685.67 cubic inches

Rounding to the nearest whole number, the volume of Kairay's sculpture is approximately 9686 cubic inches.