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). 16. find the height of the triangle sides for the triangular prism given that the surface area is 462 in². hint: there are 2 equally - sized triangles, 2 equally - sized rectangles, and 1 other rectangle.

Explanation:

Step1: Identify given values

$d = 3$ inches, $h=4$ inches

Step2: Apply lateral - surface - area formula

$SA=\pi dh=\pi\times3\times4 = 12\pi$ square inches

Step3: Calculate the numerical value

$12\pi\approx12\times 3.14 = 37.68$ square inches

Step4: Round to the nearest square inch

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

Answer:

$38$ square inches