Question

Please Help! Dimitri bought a cylindrical clay flowerpot that holds approximately 15 gallons of dry soil (1 gallon ≈ 0.15 cubic feet). The radius of the pot is 9 inches. What is the height of the flowerpot to the nearest tenth of a foot? Show your work.

Answer 1

`\huge\colorbox{blue}{h$\approx$1.3 foot }`

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

`\sf\displaystyle 1\: cubic\: foot=1728 \: cubic\: inches`

first convert gallon to cubic foot

`\sf\displaystyle 15* 0.15\: (\text{since 1 gallon=0.15 cubic feet}) \\ \displaystyle \: = 2.25`

now convert cubic feet to cubic inches:

`\sf\displaystyle 2.25* 1728 \\ = 3888`

now we need a little algebra to figure out h

`V_(cylinder)=\pi r^2 h`

substitute the value of V and r:

`\displaystyle \: \pi * {9}^(2) * h = 3888`

simplify square:

`\displaystyle \: \pi * 81 * h = 3888`

divide both sides by 81:

`\displaystyle \: ( \pi * 81 * h)/(81) = ( 3 888)/(81) \\ \pi * h = 48`

divide both sides by π:

`\displaystyle \: (\pi * h)/(\pi) = (48)/(\pi) \\ \: h \approx 15.3`

12 inches = 1 foot

15.3 " =15.3/12

≈1.3 foot