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.

1 answer

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.