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 9,682 in.3 9,682 inches cubed 19,363 in.3 19,363 inches cubed 16,747 in.3 16,747 inches cubed 7,065 in.3

1 answer

To find the volume of Kairay's sculpture, we first need to calculate the volume of the larger hemisphere with a radius of 20 inches and then subtract the volume of the smaller hemisphere with a radius of 15 inches.

The formula for the volume \( V \) of a hemisphere is given by:

\[ V = \frac{2}{3} \pi r^3 \]

For the larger hemisphere with a radius of 20 inches:

\[ V_{\text{large}} = \frac{2}{3} \pi (20^3) = \frac{2}{3} \pi (8000) = \frac{16000}{3} \pi \]

Substituting \( \pi \) with 3.14:

\[ V_{\text{large}} = \frac{16000}{3} \times 3.14 \approx 16755.56 , \text{in}^3 \]

For the smaller hemisphere with a radius of 15 inches:

\[ V_{\text{small}} = \frac{2}{3} \pi (15^3) = \frac{2}{3} \pi (3375) = \frac{6750}{3} \pi \]

Again, substituting \( \pi \) with 3.14:

\[ V_{\text{small}} = \frac{6750}{3} \times 3.14 \approx 7068.75 , \text{in}^3 \]

Now, to calculate the volume of the sculpture, we subtract the volume of the smaller hemisphere from the volume of the larger hemisphere:

\[ V_{\text{sculpture}} = V_{\text{large}} - V_{\text{small}} \approx 16755.56 - 7068.75 \approx 9686.81 , \text{in}^3 \]

Rounding this to the nearest whole number, we get:

\[ \boxed{9687 , \text{in}^3} \]

Among the options provided, the closest answer is: 9,682 inches cubed.