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)

Question

Responses

9,682 in.3
9,682 inches cubed

19,363 in.3
19,363 inches cubed

7,065 in.3
7,065 inches cubed

16,747 in.3

Answer 1

To calculate the volume of the sculpture, we need to find the volume of the larger hemisphere (radius of 20 inches) and subtract the volume of the smaller hemisphere (radius of 15 inches).

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.

For the larger hemisphere (radius = 20 inches):

\[ V_{large} = \frac{2}{3} \pi (20)^3 \] \[ = \frac{2}{3} \cdot 3.14 \cdot 8000 \] \[ = \frac{2}{3} \cdot 25120 \] \[ = \frac{50240}{3} \] \[ \approx 16746.67 \text{ cubic inches} \]

Step 2: Calculate the volume of the smaller hemisphere.

For the smaller hemisphere (radius = 15 inches):

\[ V_{small} = \frac{2}{3} \pi (15)^3 \] \[ = \frac{2}{3} \cdot 3.14 \cdot 3375 \] \[ = \frac{2}{3} \cdot 10582.5 \] \[ = \frac{21165}{3} \] \[ \approx 7055 \text{ cubic inches} \]

Step 3: Find the volume of the sculpture.

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

\[ V_{sculpture} = V_{large} - V_{small} \] \[ = 16746.67 - 7055 \] \[ \approx 9691.67 \text{ cubic inches} \]

Rounding \( 9691.67 \) to the nearest whole number gives us \( 9692 \).

Conclusion

None of the provided options match this exact result, but it appears the closest and most reasonable volume of his sculpture is rounded to:

9,682 in³ (or 9,682 inches cubed).

Please check again against your options for accuracy.