Question

1. the poster you are giving your friend is in a cardboard tube with a 2 - in. diameter and 26 - in. length. will a rectangular piece of wrapping paper that is 8 in. by 28 in. completely cover the tube? explain.

Explanation:

Step1: Find the lateral - surface area of the tube

The tube is a cylinder. The formula for the lateral - surface area of a cylinder is $A = \pi dh$, where $d$ is the diameter and $h$ is the height (or length). Given $d = 2$ in and $h=26$ in. So $A=\pi\times2\times26 = 52\pi\approx52\times3.14 = 163.28$ square inches.

Step2: Find the area of the wrapping paper

The area of a rectangle is $A = lw$, where $l$ is the length and $w$ is the width. Given $l = 28$ in and $w = 8$ in. So $A=28\times8=224$ square inches.

Step3: Compare the areas

Since $224>163.28$, the wrapping paper can cover the tube.

Answer:

Yes, because the area of the wrapping paper ($224$ square inches) is greater than the lateral - surface area of the tube ($\approx163.28$ square inches).