Answer
a. $V=64s^3$.
b. $ V=48(\pi) s^2$.
c. $V=64s^3-48(\pi) s^2$.
d. $V=16s^2(4s-3\pi)$.
e. $V=182088\;in.^3$.
Work Step by Step
The given values are
$a=4s$.
$h=48\;in.$.
$r=s$.
a.
Formula for the volume of the cube.
$\Rightarrow V_1=a^3$
Substitute the value of $a$.
$\Rightarrow V_1=(4s)^3$
Simplify.
$\Rightarrow V_1=64s^3$.
b.
Formula for the volume of the cylinder.
$\Rightarrow V_2=\pi r^2h$
Substitute the value of $h$ and $r$.
$\Rightarrow V_2=\pi (s)^2(48)$
Simplify.
$\Rightarrow V_2=48(\pi) s^2$.
c.
Metal left.
$V=V_1-V_2$
Substitute the values of volumes.
$V=64s^3-48(\pi) s^2$.
d.
Factor out common terms.
$V=16s^2(4s-3\pi)$.
e. Substitute the value of $s=15\;in.$ and $\pi=3.14$.
$V=16(15)^2(4(15)-3(3.14))$.
Use a calculator and simplify.
$V=182088\;in.^3$.
