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)

Question

Responses

4,443 in.3
4,443 inches cubed

2,221 in.3
2,221 inches cubed

555 in.3
555 inches cubed

278 in.3

Answer 1

To find the volume of a hemisphere, we can use the formula for the volume of a sphere, which is:

\[ V = \frac{4}{3} \pi r^3 \]

Since a hemisphere is half of a sphere, the volume of the hemisphere can be calculated using:

\[ V = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3 \]

First, we need to find the radius \( r \) from the diameter. The diameter is given as 10.2 inches, so the radius is:

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

Now, we can plug the radius into the hemisphere volume formula:

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

Calculating \( (5.1)^3 \):

\[ (5.1)^3 = 5.1 \times 5.1 \times 5.1 = 132.651 \text{ cubic inches} \]

Now substituting this back into our volume formula:

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

Calculating this step-by-step:

1. First, calculate \( \frac{2}{3} \times 3.14 \):

\[ \frac{2}{3} \times 3.14 \approx 2.0933 \]

2. Now, multiply by \( 132.651 \):

\[ V \approx 2.0933 \times 132.651 \approx 277.67 \text{ cubic inches} \]

3. Rounding to the nearest whole number, we get:

\[ V \approx 278 \text{ cubic inches} \]

So the answer is:

278 in.³