Question

How much broth can a bowl in the shape of a hemisphere hold? The diameter of the bowl is 10.2 inches. Use 3.14 as an approximation for pi. Round your answer to the nearest whole number. (1 point)
• 278 in.
3
• 555 in.'
0 4,443 in. 3
• 2, 221 in.

Answer 1

To find the volume of broth that a hemisphere-shaped bowl can hold, we 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 we can substitute the value of \( r \) into the volume formula:

\[
V = \frac{2}{3} \cdot 3.14 \cdot (5.1)^3
\]

First, we calculate \( (5.1)^3 \):

\[
(5.1)^3 = 5.1 \cdot 5.1 \cdot 5.1 = 132.651
\]

Now substituting back into the volume equation:

\[
V = \frac{2}{3} \cdot 3.14 \cdot 132.651
\]

Calculating \( 3.14 \cdot 132.651 \):

\[
3.14 \cdot 132.651 \approx 416.05034
\]

Now we multiply this by \( \frac{2}{3} \):

\[
V = \frac{2}{3} \cdot 416.05034 \approx 277.367
\]

Rounding to the nearest whole number, the volume of the bowl is approximately:

\[
\boxed{277} \text{ in}^3
\]

Given the provided options and rounding, the correct answer is **278 in³**.