The rectangular label will completely cover the lateral surface of the can using as little paper as possible. If the can has a height of 8 cm and a diameter of 7 cm, then what are the width and length (to the nearest centimeter) of the label?
The length of the label will be he circumference of the can.
The width of the label will be the height of the can.
Width of label=height of can=8 cm
Length of label=circumference of can=2*pi*radius or pi*diameter.
Circumference=7*pi, this is the length of the label also.
To find the width and length of the label, we need to calculate the lateral surface area of the can first.
The lateral surface area of a cylinder is given by the formula: LA = 2πrh, where r is the radius of the base of the can and h is the height.
Given that the can has a diameter of 7 cm, the radius (r) is half of the diameter, which is 7/2 = 3.5 cm. The height (h) is given as 8 cm.
Plugging these values into the formula, we get: LA = 2π(3.5 cm)(8 cm) = 56π cm² (approximately).
Now, let's calculate the width and length of the label. Since the label is a rectangle and will cover the lateral surface of the can, the width and length of the label will correspond to the circumference and height of the can, respectively.
The circumference (C) of the can is given by the formula: C = 2πr. Plugging in the value of the radius (3.5 cm), we get: C = 2π(3.5 cm) = 7π cm (approximately).
The height of the label will be the same as the height of the can, which is 8 cm.
So, the width of the label is approximately 7π cm, and the length of the label is 8 cm.
To get the measurements to the nearest centimeter, we can use the value of π as approximately 3.14.
Therefore, the width and length of the label, to the nearest centimeter, are approximately 7(3.14) cm = 22 cm and 8 cm, respectively.