Question

Linear Expressions, Equations & Inequalities Online Practice
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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 in.3
278 inches cubed

2,221 in.3
2,221 inches cubed

4,443 in.3
4,443 inches cubed

555 in.3

Answer 1

To find the volume of a bowl in the shape of a hemisphere, 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.

1. **Calculate the radius**:
The diameter of the bowl is given as 10.2 inches, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{10.2}{2} = 5.1 \text{ inches}
\]

2. **Substitute the radius into the volume formula**:
Using \( \pi \approx 3.14 \):
\[
V = \frac{2}{3} \times 3.14 \times (5.1)^3
\]

3. **Calculate \( (5.1)^3 \)**:
\[
(5.1)^3 = 5.1 \times 5.1 \times 5.1 = 132.651
\]

4. **Substitute this back into the volume equation**:
\[
V = \frac{2}{3} \times 3.14 \times 132.651
\]

5. **Calculate \( \frac{2}{3} \times 3.14 \)**:
\[
\frac{2}{3} \times 3.14 \approx 2.0933
\]

6. **Now calculate the volume**:
\[
V \approx 2.0933 \times 132.651 \approx 277.7104
\]

Rounding to the nearest whole number, the volume of the bowl is approximately **278 inches cubed**.

So the correct response is:

**278 in.³**