Answer
$V=\displaystyle \frac{4}{3}\pi x^{3}+12\pi x^{2}+36\pi x+36\pi $
Work Step by Step
$V=\displaystyle \frac{4}{3}\pi r^{3}$...the volume of a sphere with a radius r.
$r=x+3$...substitute $x+3$ with $r $in the formula.
$V=\displaystyle \frac{4}{3}\pi(x+3)^{3}$...write $(x+3)^{3}$ as $(x+3)^{2}\cdot(x+3)^{1}$.
$V=\displaystyle \frac{4}{3}\pi(x+3)^{2}\cdot(x+3)$...square the binomial.
$V=\displaystyle \frac{4}{3}\pi(x^{2}+2(x)(3)+3^{2})\cdot(x+3)$
...simplify the first parentheses.
$V=\displaystyle \frac{4}{3}\pi(x^{2}+6x+9)\cdot(x+3)$ ...distribute.
$V=\displaystyle \frac{4}{3}\pi[(x^{2}+6x+9)\cdot x+(x^{2}+6x+9)\cdot 3]$ ...distribute.
$V=\displaystyle \frac{4}{3}\pi(x^{3}+6x^{2}+9x+3x^{2}+18x+27)$ ...simplify.
$V=\displaystyle \frac{4}{3}\pi(x^{3}+9x^{2}+27x+27)$ ...distribute.
$V=\displaystyle \frac{4}{3}\pi x^{3}+12\pi x^{2}+36\pi x+36\pi $
