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 10.1 cm. the volume is $\text{cm}^{3}$. (round to the nearest tenth as needed.)

Explanation:

Step1: Substitute radius value

Substitute $r = 10.1$ into $V=\frac{4}{3}\pi r^{3}$. So $V=\frac{4}{3}\pi(10.1)^{3}$.

Step2: Calculate $(10.1)^{3}$

$(10.1)^{3}=10.1\times10.1\times10.1 = 1030.301$.

Step3: Calculate volume

$V=\frac{4}{3}\pi\times1030.301$. First, $\frac{4}{3}\times1030.301\approx1373.735$. Then $V\approx1373.735\times\pi\approx4317.1$.

Answer:

$4317.1$