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

1 answer

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 and \( \pi \approx 3.14 \).

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

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

  2. Calculate the volume using the radius: Substitute \( r \) and \( \pi \) into the volume formula:

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

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

  4. Plug this value into the volume formula: \[ V = \frac{2}{3} \times 3.14 \times 132.651 \] \[ V = \frac{2 \times 3.14 \times 132.651}{3} \]

  5. Calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \]

  6. Multiply by \( 132.651 \): \[ 6.28 \times 132.651 \approx 833.773 \]

  7. Divide by 3: \[ V \approx \frac{833.773}{3} \approx 277.924 \]

  8. Round to the nearest whole number: The volume of the bowl is approximately 278 cubic inches.

Thus, the bowl can hold approximately 278 cubic inches of broth.