Question

A label is placed around a soup can during manufacturing. If the label is represented by the rectangle in the figure, how many square inches is the label? Answer in terms of π.

image of a net drawing of a cylinder is shown as two circles each with a radius labeled 4 inches and a rectangle with a height labeled 7.6 inches

60.8π square inches
92.8π square inches
32π square inches
29.6π square inches

Answer 1

60.8π square inches

Step-by-step explanation:

Chain of thought reasoning: 1. The label is represented by the rectangle in the figure.

2. The area of a rectangle is equal to the width multiplied by the height or A = w x h.

3. The width of the rectangle is equal to the circumference of the circles.

4. The circumference of a circle is equal to 2πr, where r is the radius of the circle.

5. Therefore, the width of the rectangle is equal to 2π x 4 = 8π inches.

6. The height of the rectangle is 7.6 inches.

7. Therefore, the area of the rectangle is equal to 8π x 7.6 = 60.8π square inches.

Answer 2

60.8π square inches.

Explanation:

The label is a rectangle that will be wrapped around a cylinder. So, the area of the label can be found by multiplying the height of the rectangle by the circumference of the cylinder. The circumference of the cylinder can be found by multiplying the diameter by π. Since the two circles in the figure represent the top and bottom faces of the cylinder, the diameter is 2 × 4 = 8 inches. Therefore, the circumference of the cylinder is 8π inches. Thus, the area of the label is:

7.6 × 8π = 60.8π square inches

Therefore, the label is 60.8π square inches.