Question

A can of carrots has a diameter of 2.5 inches and a height of 3.5 inches. How many square inches of paper will be needed for the label on

the outside of the can? Use 3.14 for pi and round your answer to the nearest inch. (1 point)
35 in.²
O 24 in.²
O 27 in.²
O 67 in.²

Answer 1

To find the surface area of the can, we calculate the area of the circles (top and bottom) and the area of the curved side. The total surface area is the sum of these areas.

Step-by-step explanation:

To find the surface area of the can, we need to calculate the area of the top and bottom circles, as well as the area of the curved side. Let's start with the circles:

The formula for the area of a circle is A = πr². Since the diameter is given, we divide it by 2 to find the radius:

r = 2.5 inches / 2 = 1.25 inches

Now we can calculate the area of the circles:

A = π(1.25 inches)² = 4.91 square inches

Next, we calculate the area of the curved side. This is essentially a rectangle that has been wrapped around the can. The width of the rectangle is the height of the can (3.5 inches), and the length is the circumference of the circle at the top (since it's the same as the circumference at the bottom).

The formula for the circumference of a circle is C = 2πr:

C = 2π(1.25 inches) = 7.85 inches

Now we can calculate the area of the side:

A = 7.85 inches × 3.5 inches = 27.48 square inches

To find the total surface area, we sum the areas of the circles and the side:

Total surface area = 2(A_circle) + A_side = 2(4.91 square inches) + 27.48 square inches = 37.3 square inches

Rounding to the nearest inch, the label will require approximately 37 square inches of paper.

Answer 2

To find the amount of paper needed for a can's label, calculate the lateral surface area: A = 2πrh. Using the diameter (2.5 inches) and height (3.5 inches) of the can, we find the required amount of paper is approximately 27 square inches.

Step-by-step explanation:

The question asks for the amount of paper needed for the label of a can of carrots. To determine this, we need to calculate the surface area for the label which will align with the lateral surface of the cylinder-shaped can. The lateral surface area of the cylinder is given by the formula A = 2πrh.

First, we find the radius by dividing the diameter by 2: 2.5 inches ÷ 2 = 1.25 inches. Then we plug the radius and the height into the formula: A = 2 × 3.14 × 1.25 inches × 3.5 inches.

Next, we calculate: A = 2 × 3.14 × 1.25 inches × 3.5 inches = 27.5 square inches. Rounding to the nearest inch, we get that the label will need approximately 27 square inches of paper.