Question

v = \frac{4}{3}\pi r^{3}
the formula gives the volume v of a sphere with radius r. what is the volume, in cubic feet, of a sphere with a radius of 2 feet?
choose 1 answer:
a 4\pi
b 8\pi
c \frac{8}{3}\pi
d \frac{32}{3}\pi

Explanation:

Step1: Substitute radius value

Given $r = 2$ into $V=\frac{4}{3}\pi r^{3}$, we get $V=\frac{4}{3}\pi\times(2)^{3}$.

Step2: Calculate the cube of radius

$(2)^{3}=2\times2\times2 = 8$, so $V=\frac{4}{3}\pi\times8$.

Step3: Multiply the fractions and $\pi$

$\frac{4}{3}\times8=\frac{32}{3}$, then $V = \frac{32}{3}\pi$.

Answer:

D. $\frac{32}{3}\pi$