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 of pi. Round your answer to the nearest whole number.

1 answer

To find out how much broth a bowl in the shape of a hemisphere can hold, we need to calculate the volume of the hemisphere. The formula for the volume \( V \) of a hemisphere is given by:

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

where \( r \) is the radius of the hemisphere.

Given that the diameter of the bowl is 10.2 inches, we can find the radius by dividing the diameter by 2:

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

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

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

First, we need to calculate \( (5.1)^3 \):

\[ (5.1)^3 = 5.1 \times 5.1 \times 5.1 \] Calculating step by step:

  1. \( 5.1 \times 5.1 = 26.01 \)
  2. \( 26.01 \times 5.1 = 132.651 \)

So, \( (5.1)^3 \approx 132.651 \).

Now substitute this back into the volume formula:

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

Calculating \( 3.14 \times 132.651 \):

\[ 3.14 \times 132.651 \approx 416.77334 \]

Now compute the full volume:

\[ V = \frac{2}{3} \times 416.77334 \approx 278.51556 \]

Finally, round this to the nearest whole number:

\[ V \approx 279 \]

Thus, the bowl can hold approximately 279 cubic inches of broth.