Answer
a)$V=$$(4s)^3$
b) $V=48$$\pi$$s^2$
c)$V=$$(4s)^3$$-$$48$$\pi$$s^2$
d)$V=$$(4s)$$(4s^2$$-$$12$$\pi$$)$
e)$V=$$182,088$$ in^2$
Work Step by Step
a)The formula for the volume of a cube is $l$$\times$$w$$\times$$h$, so $4s$$\times$$4s$$\times$$4s$ =$(4s)^3$.
b) The volume of a cylinder is $\pi$$r^2$$h$ so $V=48$$\pi$$s^2$
c)The volume of the cylinder has to be subtracted from the volume of the cube, so $V=$$(4s)^3$$-$$48$$\pi$$s^2$
d)The Greatest Common Factor of the two terms in part c is $4s$, so $V=4s($$(4s)^2$$-$$12$$\pi$$s)$.
e)Plug and chug the given values into the new simplified equation: $V=4(15)($$(4(15))^2$$-$$12(3.14)(15))$$=182,088$$ in^2$
