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
To determine the surface area of the can, we need to calculate the area of the curved surface and the top and bottom circular surfaces of the can.
The curved surface area of a cylinder can be found by multiplying the height of the cylinder by the circumference of the base. The circumference can be calculated using the formula: C = πd, where C is the circumference and d is the diameter.
The height of the can is 3.5 inches and the diameter is 2.5 inches, so the circumference is C = π * 2.5 = 7.85 inches.
The curved surface area of the can is therefore 3.5 * 7.85 = 27.475 square inches.
The top and bottom surfaces of the can are circles, so we need to calculate the area of one circle and then multiply it by 2 to account for both ends.
The area of a circle can be found using the formula: A = πr^2, where A is the area and r is the radius. The radius is half of the diameter, so r = 2.5 / 2 = 1.25 inches.
The area of one circle is therefore π * 1.25^2 = 4.91 square inches.
Multiplying this by 2 gives us 2 * 4.91 = 9.82 square inches for both ends.
Therefore, the total surface area of the can is 27.475 + 9.82 = 37.295 square inches.
So, we will need approximately 37.295 square inches of paper for the label on the outside of the can.