A can of beans has a radius of 3 inches and a height of 4.5 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.
a. 24 inches squared
b.80 inches squared
c.42 inches squared
d. 85 inches squared
To find the surface area of the label on the outside of the can, we need to find the area of the curved part of the can (the lateral surface area) and the area of the circular top and bottom.
The lateral surface area of a cylinder is given by the formula L = 2πrh, where r is the radius and h is the height.
In this case, the radius is 3 inches and the height is 4.5 inches.
So, the lateral surface area is L = 2 * 3.14 * 3 * 4.5 = 84.78 inches squared (rounded to the nearest inch, this is 85 inches squared).
The area of each circular top and bottom is given by the formula A = πr^2.
In this case, the radius is 3 inches.
So, the area of each circular top and bottom is A = 3.14 * 3^2 = 28.26 inches squared (rounded to the nearest inch, this is 28 inches squared).
To find the total surface area of the label, we add the lateral surface area to twice the area of each circular top and bottom:
Total surface area = L + 2A = 85 + 2 * 28 = 141 inches squared (rounded to the nearest inch).
Therefore, the answer is not provided in the options.