Question

the volume of a sphere is a function of its radius, $v = \frac{4}{3}\pi r^3$. evaluate the function for the volume of a volleyball with radius 10.7 cm. the volume is \\(\square\\) \\(\mathrm{cm}^3\\). (round to the nearest tenth as needed.)

Explanation:

Step1: Identify the formula and given value

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \), and the radius \( r = 10.7\space cm \).

Step2: Substitute the radius into the formula

Substitute \( r = 10.7 \) into the formula: \( V=\frac{4}{3}\pi(10.7)^{3} \).
First, calculate \( (10.7)^{3}=10.7\times10.7\times10.7 = 1225.043 \).
Then, \( \frac{4}{3}\pi\times1225.043=\frac{4\times1225.043\times\pi}{3} \).
Calculate \( 4\times1225.043 = 4900.172 \), so \( V=\frac{4900.172\times\pi}{3} \).
Using \( \pi\approx3.1416 \), we get \( V=\frac{4900.172\times3.1416}{3} \).
Calculate \( 4900.172\times3.1416\approx15393.7 \), then \( V\approx\frac{15393.7}{3}\approx5131.2 \).

Answer:

\( 5131.2 \)