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) Responses 278 in3 278 in3 2,221 in3 2,221 in3 555 in3 555 in3 4,443 in3

Answer 1

To find out how much broth 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.

First, we need to find the radius:

The diameter of the bowl is 10.2 inches, so the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{10.2}{2} = 5.1 \text{ inches}
\]

Now, substitute the radius into the volume formula using \( \pi \approx 3.14 \):

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

Calculating \( (5.1)^3 \):

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

Now plug it back into the volume formula:

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

Calculating the product:

\[
3.14 \times 132.651 \approx 416.84934
\]

Then multiply by \(\frac{2}{3}\):

\[
V = \frac{2}{3} \times 416.84934 \approx 278.89956
\]

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

\[
\boxed{279} \text{ in}^3
\]

However, since this doesn't match any of your options (278 in³, 2,221 in³, 555 in³, 4,443 in³), based on the calculations, the closest rounded value is 278 in³. Thus it appears the best choice provided is:

\[
\boxed{278} \text{ in}^3
\]