Answer:
[tex]\huge\colorbox{blue}{h$\approx$1.3 foot }[/tex]
Step-by-step explanation:
we are given volume and redious
but r is in inches and V is in gallons
so we have to convert V into inches unit
[tex] \sf\displaystyle 1\: cubic\: foot=1728 \: cubic\: inches[/tex]
first convert gallon to cubic foot
[tex] \sf\displaystyle 15\times 0.15\: (\text{since 1 gallon=0.15 cubic feet}) \\ \displaystyle \: = 2.25[/tex]
now convert cubic feet to cubic inches:
[tex]\sf\displaystyle 2.25\times 1728 \\ = 3888[/tex]
now we need a little algebra to figure out h
[tex]V_{cylinder}=\pi r^2 h[/tex]
substitute the value of V and r:
[tex] \displaystyle \: \pi \times {9}^{2} \times h = 3888[/tex]
simplify square:
[tex] \displaystyle \: \pi \times 81 \times h = 3888[/tex]
divide both sides by 81:
[tex] \displaystyle \: \frac{ \pi \times 81 \times h}{81} = \frac{ 3 888}{81} \\ \pi \times h = 48[/tex]
divide both sides by π:
[tex] \displaystyle \: \frac{\pi \times h}{\pi} = \frac{48}{\pi} \\ \: h \approx 15.3[/tex]
12 inches = 1 foot
15.3 " =15.3/12
≈1.3 foot
