Question

What must the height of a cylindrical 750-gal tank if it is 4ft in diameter? (1ft^3 = 7.48gal) Round to the nearest inch.

Answer 1

well, we know that 1ft³ = 7.48 gallons, alright, we have a volume in gallons and a diameter in feet, so if we were to use the diameter in feet to get the volume what we would end up will be a volume in ft³, so let's convert firstly the gallons to ft³ then

$750g\cdot \cfrac{ft^3}{7.48g}\implies 750g\cdot \cfrac{ft^3}{~~\frac{748}{100}g~~}\implies \cfrac{18750}{187}ft^3$

why do I use a fraction? for the sake of not losing value in the rounding, so let's use the fraction for the volume of a right-circular cylinder

$\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} h=height\\ r=radius\\[-0.5em] \hrulefill\\ r = \stackrel{\textit{half diameter}}{2}\\ V=\frac{18750}{187} \end{cases}\implies \cfrac{18750}{187}=\pi (2)^2h \\\\\\ \cfrac{18750}{187(4\pi )}=h\implies \stackrel{ft}{7.979}~\approx~h\implies \stackrel{\textit{converting to inches}}{7.979\cdot 12\approx h}\implies \stackrel{\textit{rounded up}}{\stackrel{in}{96}\approx h}$