Question

a beach ball has a diameter of 18 inches. what is the approximate volume, rounded to the nearest whole number, of the inflated beach ball? use 3.14 for π. 1,017 in.³ 3,052 in.³ 9,156 in.³ 24,417 in.³

Explanation:

Step1: Find the radius

The diameter of the beach ball is 18 inches. The radius \( r \) is half of the diameter, so \( r=\frac{18}{2} = 9 \) inches.

Step2: Use the volume formula for a sphere

The volume \( V \) of a sphere is given by the formula \( V=\frac{4}{3}\pi r^{3} \). We are using \( \pi = 3.14 \) and \( r = 9 \). Substitute these values into the formula:
\( V=\frac{4}{3}\times3.14\times9^{3} \)
First, calculate \( 9^{3}=9\times9\times9 = 729 \).
Then, \( \frac{4}{3}\times3.14\times729 \).
First, \( \frac{4}{3}\times729 = 4\times243=972 \).
Then, \( 972\times3.14 = 3051.48 \approx 3052 \) (rounded to the nearest whole number).

Answer:

B. \( 3,052\ \text{in.}^3 \)