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

Answer:

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

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

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

first convert gallon to cubic foot

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

now convert cubic feet to cubic inches:

$\sf\displaystyle 2.25\times 1728 \\ = 3888$

now we need a little algebra to figure out h

$V_{cylinder}=\pi r^2 h$

substitute the value of V and r:

$\displaystyle \: \pi \times {9}^{2} \times h = 3888$

simplify square:

$\displaystyle \: \pi \times 81 \times h = 3888$

divide both sides by 81:

$\displaystyle \: \frac{ \pi \times 81 \times h}{81} = \frac{ 3 888}{81} \\ \pi \times h = 48$

divide both sides by π:

$\displaystyle \: \frac{\pi \times h}{\pi} = \frac{48}{\pi} \\ \: h \approx 15.3$

12 inches = 1 foot

15.3 " =15.3/12

≈1.3 foot