?A cylindrical garbage can has a radius of 1.5 feet and holds approximately 28.27 cubic feet of trash. Find the approximate height of the garbage can.

Question

a. 3.0 ft

b. 4.0 ft

c. 2.0 ft

d. 6.0 ft

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Answer 1 · 2018-05-16T10:26:42

$b .$ $"b".$ $4.0 ft$ $"4.0 ft"$

The formula for the volume of a cylinder is:

$V = π \cdot r^{2} \cdot h$ $V=pi*r^2*h$ ,

where:

$V$ $V$ is volume, $π$ $pi$ is pi, $r$ $r$ is the radius, and $h$ $h$ is height.

Known

$V = {28.27 ft}^{3}$ $V= "28.27 ft"^3"$

$π = 3.14159$ $pi= "3.14159$ (or you can use the $π$ $pi$ key on your calculator)

$r = 1.5 ft$ $r="1.5 ft"$

$r^{2} = {2.25 ft}^{2}$ $r^2="2.25 ft" ^2"$

Rearrange the formula to isolate height. Plug in the known values and solve.

$h = \frac{V}{π \cdot r^{2}}$ $h=(V)/(pi*r^2)$

$h=(28.27cancel"ft"^3)/(pi*2.25cancel "ft"^2)="4.00 ft"$ rounded to two decimal places