To find the volume of a bowl in the shape of a hemisphere, you can use the formula for the volume of a hemisphere:
\[ V = \frac{2}{3} \pi r^3 \]
where \( r \) is the radius of the hemisphere. The radius is half of the diameter.
Given that the diameter of the bowl is 10.2 inches, the radius \( r \) is:
\[ r = \frac{10.2}{2} = 5.1 \text{ inches} \]
Now, substituting the radius and using 3.14 for \( \pi \):
\[ V = \frac{2}{3} \times 3.14 \times (5.1)^3 \]
Calculating \( (5.1)^3 \):
\[ (5.1)^3 = 5.1 \times 5.1 \times 5.1 = 132.651 \]
Now substituting back into the volume formula:
\[ V = \frac{2}{3} \times 3.14 \times 132.651 \]
Calculating this step by step:
- \( 3.14 \times 132.651 \approx 416.03634 \)
- \( \frac{2}{3} \times 416.03634 \approx 277.35756 \)
Rounding \( 277.35756 \) to the nearest whole number gives:
\[ \approx 278 \text{ inches cubed} \]
The correct answer is:
278 in.³