Question

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. Round your answer to the nearest whole number.(1 point) Responses 7,065 in.3 7,065 inches cubed 16,747 in.3 16,747 inches cubed 9,682 in.3 9,682 inches cubed 19,363 in.3 19,363 inches cubed

Answer 1

To calculate the volume of Kairay's sculpture, we need to find the volume of the larger hemisphere and then subtract the volume of the smaller hemisphere from it.

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

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

### Step 1: Calculate the volume of the larger hemisphere (radius = 20 inches)

Using \( r = 20 \) inches:

\[
V_{large} = \frac{2}{3} \cdot 3.14 \cdot (20)^3
\]

Calculating \( (20)^3 \):

\[
20^3 = 8000
\]

Now substituting back into the volume formula:

\[
V_{large} = \frac{2}{3} \cdot 3.14 \cdot 8000
\]
\[
V_{large} = \frac{2 \cdot 3.14 \cdot 8000}{3}
\]
\[
V_{large} = \frac{50240}{3} \approx 16746.67
\]

### Step 2: Calculate the volume of the smaller hemisphere (radius = 15 inches)

Using \( r = 15 \) inches:

\[
V_{small} = \frac{2}{3} \cdot 3.14 \cdot (15)^3
\]

Calculating \( (15)^3 \):

\[
15^3 = 3375
\]

Now substituting back into the volume formula:

\[
V_{small} = \frac{2}{3} \cdot 3.14 \cdot 3375
\]
\[
V_{small} = \frac{2 \cdot 3.14 \cdot 3375}{3}
\]
\[
V_{small} = \frac{21225}{3} \approx 7075
\]

### Step 3: Calculate the volume of the sculpture

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

\[
V_{sculpture} = V_{large} - V_{small}
\]
\[
V_{sculpture} \approx 16746.67 - 7075 \approx 9671.67
\]

Rounding to the nearest whole number, we find:

\[
V_{sculpture} \approx 9682 \text{ in}^3
\]

Thus, the volume of Kairay's sculpture is approximately **9,682 inches cubed**.