Question

katie wants to make a container that is in the shape of a large cylinder tube that she can use to display and store the sea shells she has collected. she has a large piece of clear flexible plastic that she is going to cut into a rectangle. she is then going to use this rectangle to make a cylinder-shaped tube by rolling the ends of the rectangle together and taping them. she will then make circular covers to go on either end of the cylinder tube so that it can be used as a container.
the cylinder tube needs to have a height of 15 inches high and a volume of 2,309 square inches.
if the height of the rectangle she is going to use is 15 inches, then what length, rounded to the nearest inch, does the rectangle need to be?
$square$ inches

Explanation:

Step1: Recall cylinder volume formula

The volume of a cylinder is $V = \pi r^2 h$, where $V=2309$, $h=15$.

Step2: Solve for radius $r$

Rearrange to solve for $r^2$:
$r^2 = \frac{V}{\pi h} = \frac{2309}{\pi \times 15}$
Calculate the value:
$r^2 = \frac{2309}{47.1239} \approx 49$
Take square root: $r \approx 7$ inches

Step3: Find rectangle length (circumference)

The length of the rectangle equals the circumference of the circular base: $C = 2\pi r$
Substitute $r=7$:
$C = 2 \times \pi \times 7 = 14\pi \approx 43.98$

Step4: Round to nearest inch

Round 43.98 to the nearest whole number.

Answer:

44 inches