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.
-
Calculate the radius:
The diameter of the bowl is 10.2 inches, so the radius \( r \) is:\[ r = \frac{10.2}{2} = 5.1 \text{ inches} \]
-
Calculate the volume:
Substitute \( r = 5.1 \) inches and \( \pi \approx 3.14 \) into the volume formula:\[ V = \frac{2}{3} \times 3.14 \times (5.1)^3 \]
First, calculate \( (5.1)^3 \):
\[ (5.1)^3 = 5.1 \times 5.1 \times 5.1 = 132.651 \]
Now substitute this value into the volume formula:
\[ V = \frac{2}{3} \times 3.14 \times 132.651 \]
Calculate \( 3.14 \times 132.651 \):
\[ 3.14 \times 132.651 \approx 416.10634 \]
Now, take \( \frac{2}{3} \) of that result:
\[ V \approx \frac{2}{3} \times 416.10634 \approx 277.40422667 \]
-
Round to the nearest whole number:
\[ V \approx 277 \]
Thus, to the nearest whole number, the bowl can hold approximately 278 inches cubed.
So the correct response is:
278 in.³ (278 inches cubed).