Question

1. what is the volume of this beach ball if its width is 24 inches? (use 3.14 for $\pi$) \

57,905.84 $\text{in}^3$ \
904.78 $\text{in}^3$ \
375.69 $\text{in}^3$ \
7,234.56 $\text{in}^3$

Explanation:

Step1: Determine the radius

The width of the beach ball (a sphere) is its diameter. So, diameter \( d = 24 \) inches. Radius \( r=\frac{d}{2}=\frac{24}{2} = 12 \) inches.

Step2: Use the sphere volume formula

The volume \( V \) of a sphere is given by \( V=\frac{4}{3}\pi r^{3} \). Substitute \( \pi = 3.14 \) and \( r = 12 \):
\( V=\frac{4}{3}\times3.14\times12^{3} \)
First, calculate \( 12^{3}=12\times12\times12 = 1728 \).
Then, \( \frac{4}{3}\times3.14\times1728 = 4\times3.14\times576 \) (since \( \frac{1728}{3}=576 \))
\( 4\times3.14 = 12.56 \), then \( 12.56\times576 = 7234.56 \) cubic inches.

Answer:

7,234.56 in³