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)
Responses
24 in.2
24 in.2
27 in.2
27 in.2
35 in.2
35 in.2
67 in.2
67 in.2
To find the surface area of the label on the outside of the can, we need to calculate the surface area of the curved part of the can, which is a cylinder, and the surface area of the top and bottom, which are circles.
The surface area of the curved part of the can is given by the formula:
Surface Area = 2 * pi * r * h
where r is the radius of the can (half of the diameter) and h is the height.
Given that the diameter of the can is 2.5 inches, the radius (r) is 2.5/2 = 1.25 inches.
The height (h) of the can is 3.5 inches.
Using pi = 3.14, we can calculate the surface area of the curved part of the can as:
Surface Area = 2 * 3.14 * 1.25 * 3.5 = 27.65 square inches (rounded to the nearest inch).
The surface area of each circle, which represents the top and bottom of the can, is given by the formula:
Surface Area = pi * r^2
So, the surface area of each circle is:
Surface Area = 3.14 * 1.25^2 = 4.91 square inches (rounded to the nearest inch).
Since there are two circles (top and bottom) on the can, the total surface area of the circles is 2 * 4.91 = 9.82 square inches (rounded to the nearest inch).
The total surface area of the label on the outside of the can is the sum of the surface area of the curved part and the surface area of the circles:
Total Surface Area = Surface Area of Curved Part + Surface Area of Circles
Total Surface Area = 27.65 + 9.82 = 37.47 square inches (rounded to the nearest inch).
Therefore, the answer is 37 square inches.