Question

Jesse wants to gift wrap a cylindrical pencil case that has a radius of 1.5 inches and a height of 8 inches. What is the area of the paper she will need to cover the entire surface?

Answer 1

28.5 pi square inches

Explanation:

The surface area of a cylinder is the lateral area plus two times the area of the base circle. The lateral area is the perimeter of the base circle times the height, and the perimeter of a circle is 2*pi*r.

Therefore the lateral area is:

LA = Perimeter*Height

= 2*pi*r*h

= 2*pi*1.5*8

= 24pi

The base area would be A = pi*r*r since the bases of cylinders are circles.

BA = pi*r*r

= pi*1.5*1.5

= 2.25 pi

Since there are two circles (top AND bottom) in a cylinder, the final surface area of the cylinder would be:

SA = LA + 2BA

= 24pi + 2*2.25pi

= 24pi + 4.5pi

= 28.5 pi

Answer 2

Jesse will need about 89.5 square inches of gift wrap.

Explanation:

We need to find the amount of wrapping paper that will cover the entire outside surface of the cylindrical gift. This means that we need to find its surface area, which is the total area an object's surface occupies.

The formula for cylinder surface area is as follows:

`A=2\pi rh+2\pi r^(2)` (where r = radius and h = height)

In this case, the radius, or r, is 1.5 in, and the height, or h, is 8 in. Plugging these values into our formula, we get a total surface area of:

`A=2\pi rh+2\pi r^(2)\\= 2\pi *1.5*8+2\pi * 1.5^(2) \\= 24\pi +4.5\pi \\=28.5\pi \\ \approx \text{\bf 89.5 \bf $in^(2)$ }`

Hope this helps!