Question

the oatmeal box shown is shaped like a cylinder. use a net to find the surface area s of the oatmeal box, rounded to the nearest tenth. then find the number of square feet of cardboard needed for 1,500 oatmeal boxes, rounded to the nearest whole number. use 3.14 for π.
image of a cylinder labeled oatmeal 9 in. with a radius of 4 in.
the surface area is about square square inches.
the number of square feet of cardboard needed is about square.

Explanation:

Step1: Recall the formula for the surface area of a cylinder

The surface area \( S \) of a cylinder is given by the formula \( S = 2\pi r^2 + 2\pi rh \), where \( r \) is the radius and \( h \) is the height.
Here, \( r = 4 \) inches and \( h = 9 \) inches, and \( \pi \approx 3.14 \).

Step2: Calculate the area of the two circular bases

The area of one circular base is \( \pi r^2 \), so for two bases, it is \( 2\pi r^2 \).
Substituting \( r = 4 \) and \( \pi = 3.14 \):
\( 2\times3.14\times4^2 = 2\times3.14\times16 = 100.48 \) square inches.

Step3: Calculate the lateral (curved) surface area

The lateral surface area is \( 2\pi rh \).
Substituting \( r = 4 \), \( h = 9 \), and \( \pi = 3.14 \):
\( 2\times3.14\times4\times9 = 226.08 \) square inches.

Step4: Calculate the total surface area

Add the area of the two bases and the lateral surface area:
\( S = 100.48 + 226.08 = 326.56 \) square inches. Rounding to the nearest tenth gives \( 326.6 \) square inches.

Step5: Calculate the total cardboard for 1500 boxes

Multiply the surface area of one box by 1500:
\( 326.56\times1500 = 489840 \) square inches.

Step6: Convert square inches to square feet

Since 1 square foot = 144 square inches, divide the total square inches by 144:
\( \frac{489840}{144} = 3401.666\cdots \) Rounding to the nearest whole number gives 3402 square feet.

Answer:

The surface area is about \( 326.6 \) square inches.
The number of square feet of cardboard needed is about \( 3402 \).