Question

Given that the volume of a sphere varies as the cube of its radius, and that when the radius is $3\frac{1}{2}$ feet the volume is $179\frac{2}{3}$ cubic feet, find the volume when the radius is $1foot9inches$.

Answer 1

Let $V$ be the volume and $r$ be the radius.

According to question let,

$V=k.r^3$

Where $k$ is a constant,

Given $V=179.5$ we have $r=3.5$ So,

$179.5=k.(3.5{)}^3$

$k=\frac{179.5}{42.875}=4.19$

$V=\left(4.19\right)r^3$

$1$ foot $9$ inches is $1.75$ feet. So for $r=1.75$ feet

$V=\left(4.19\right)(1.75{)}^3$

$V=22.45$ cubic feet