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.

Answer 1

To calculate the volume of the sculpture, we must find the volume of the larger hemisphere and subtract the volume of the smaller hemisphere that has been removed.

The volume of a hemisphere is given by the formula:

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

where \( r \) is the radius of the hemisphere.

First, let's calculate the volume of the larger hemisphere (with a radius of 20 inches):

\[ V_{\text{large}} = \frac{2}{3} \pi (20)^3 \]
\[ V_{\text{large}} = \frac{2}{3} \times 3.14 \times (20 \times 20 \times 20) \]
\[ V_{\text{large}} = \frac{2}{3} \times 3.14 \times 8000 \]
\[ V_{\text{large}} = \frac{2}{3} \times 25120 \]
\[ V_{\text{large}} = 16746.6667 \; \text{in}^3 \]

Next, we need to calculate the volume of the smaller hemisphere (with a radius of 15 inches):

\[ V_{\text{small}} = \frac{2}{3} \pi (15)^3 \]
\[ V_{\text{small}} = \frac{2}{3} \times 3.14 \times (15 \times 15 \times 15) \]
\[ V_{\text{small}} = \frac{2}{3} \times 3.14 \times 3375 \]
\[ V_{\text{small}} = \frac{2}{3} \times 10593.75 \]
\[ V_{\text{small}} = 7058.5 \; \text{in}^3 \]

Now, we subtract the volume of the smaller hemisphere from the volume of the larger hemisphere to obtain the volume of Kairay's sculpture:

\[ V_{\text{sculpture}} = V_{\text{large}} - V_{\text{small}} \]
\[ V_{\text{sculpture}} = 16746.6667 \; \text{in}^3 - 7058.5 \; \text{in}^3 \]
\[ V_{\text{sculpture}} = 9688.1667 \; \text{in}^3 \]

Rounded to the nearest whole number:

\[ V_{\text{sculpture}} \approx 9688 \; \text{in}^3 \]

Therefore, the volume of Kairay's sculpture is approximately 9688 cubic inches.

Answer 2

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