Question

1. a manufacturer of canned fruit products is making a new label for its canned fruit salad. the can is 4 inches tall and has a diameter of 3 inches. determine the size of the label needed to cover the sides of the can to the nearest square inch. hint: we are concerned only about the side or lateral portion of the can, not the top or bottom (sa = πdh, formula for lateral surface area of a cylinder).

Explanation:

Step1: Identify the values of d and h

Given $d = 3$ inches and $h=4$ inches.

Step2: Apply the lateral - surface - area formula

The formula for the lateral surface area of a cylinder is $SA=\pi dh$. Substitute $d = 3$ and $h = 4$ into the formula: $SA=\pi\times3\times4=12\pi$.

Step3: Calculate the numerical value

Using $\pi\approx3.14$, we have $SA\approx12\times3.14 = 37.68$.

Step4: Round to the nearest square inch

Rounding $37.68$ to the nearest square inch gives $38$.

Answer:

38 square inches