Question

A gift box in the shape of a cylinder has a diameter of 8 inches and a height of 12 inches. Which measurement is closest to the total surface area of the gift box in square inches?

Answer 1

Case: Total surface area of a cylinder

Given:

The cylinder has a diameter of 8 inches and a height of 12 inches.

d= 8 in

h= 12 in

Required: To find the Total surface area of a cylinder

Method:

Step 1: Recall the formula for Total surface area of a cylinder

`\begin{gathered} T=2\pi rh+2\pi r^2 \\ T=2\pi r(h+r) \end{gathered}`

Step 2: Next, we get the radius from the given diameter

radius= diameter/2

r= 8/2

r= 4in

Step 3: Finally we input the given variables

`\begin{gathered} T=2\pi(4)[12+4] \\ T=2\pi(4)(16) \\ T=128\pi \\ T=402.12 \end{gathered}`

Final answer: Rounded to 2 decimal places

The Total Surface Area of the Cylinder is 402.12 square inches.