#24. You are a math teacher who is trying to make math more fun by relating it to things in the real world. You brought a basketball to your classroom and asked your students to find the volume (rounded to the nearest whole number) of the basketball if its radius is 4.5 inches.

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Answer 1

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

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

where \( V \) is the volume and \( r \) is the radius.

Given that the radius \( r \) of the basketball is 4.5 inches, we can plug that value into the formula:

\[ V = \frac{4}{3} \pi (4.5)^3 \]

First, we calculate \( (4.5)^3 \):

\[ (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 91.125 \]

Now, we can substitute this value back into the volume formula:

\[ V \approx \frac{4}{3} \times \pi \times 91.125 \]

Now, choose the approximation for \( \pi \) (using \( \pi \approx 3.14 \)):

\[ V \approx \frac{4}{3} \times 3.14 \times 91.125 \]

Calculating \( \frac{4}{3} \times 3.14 \) first:

\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]

Now, multiply this by \( 91.125 \):

\[ V \approx 4.18667 \times 91.125 \approx 381.701 \]

Finally, rounding to the nearest whole number:

\[ V \approx 382 \]

So, the volume of the basketball is approximately 382 cubic inches. If you have specific answer choices, feel free to share them for further assistance!