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

Explanation:

Step1: Substitute radius into formula

Substitute $r=11.5$ into $V=\frac{4}{3}\pi r^3$:
$$V=\frac{4}{3}\pi (11.5)^3$$

Step2: Calculate cube of radius

Compute $11.5^3$:
$$11.5^3=11.5\times11.5\times11.5=1520.875$$

Step3: Multiply by $\frac{4}{3}\pi$

Calculate the product:
$$V=\frac{4}{3}\pi\times1520.875\approx\frac{4\times3.1416\times1520.875}{3}$$
$$V\approx\frac{19123.11}{3}\approx6374.4$$

Answer:

$6374.4$ cm³