Questions: Is 700 cubic inches of air enough to fill a beach ball with a radius of 6 inches? Enter the volume of the ball. Use 3.14 for an approximation. Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest whole number as needed.) A. No, because the volume of the ball is cubic inches and there is not enough air to fill the ball. B. Yes, because the volume of the ball is cubic inches and there is enough air to fill the ball.

Solution Steps

To determine if 700 cubic inches of air is enough to fill a beach ball with a radius of 6 inches, we need to calculate the volume of the ball using the formula for the volume of a sphere, \( V = \frac{4}{3} \pi r^3 \). We will use 3.14 as an approximation for \(\pi\). After calculating the volume, we will compare it to 700 cubic inches to determine if it is sufficient.

To find the volume \( V \) of a sphere, we use the formula:

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

Substituting \( r = 6 \) inches and using \( \pi \approx 3.14 \):

\[ V = \frac{4}{3} \times 3.14 \times (6)^3 \]

Calculating \( (6)^3 = 216 \):

\[ V = \frac{4}{3} \times 3.14 \times 216 \approx 904.32 \]

Rounding \( 904.32 \) to the nearest whole number gives:

\[ V \approx 904 \text{ cubic inches} \]

We need to determine if \( 700 \) cubic inches of air is sufficient to fill the beach ball. Since:

\[ 700 < 904 \]

it is clear that there is not enough air to fill the ball.

Final Answer