Question

The area of the sheet of wrapping paper is equal to the lateral surface area of a cylindrical tube.

The tube is 14 inches tall. What is the surface area of the tube, including the bases?

Explain your reasoning.

Answer 1

Step 1: Total surface area of cylindrical tube = lateral surface area + area of bases

Step 2: Given that: Height of cylindrical tube $=14inches$

Circumference of cylindrical tube $=26inches$

$$\begin{gathered} 2\pi r=26inches \\ 2\times 3.14\times r=26 \\ r=4.1inches \end{gathered}$$

Step 3: Total surface area of cylindrical tube $=2{\mathrm{\pi r}}^2+2\mathrm{\pi rh}$

$$\begin{gathered} =2(3.14\times 4.1\times 4.1+3.14\times 4.1\times 14) \\ =2(52.78+180.23)sq.inches \\ =2\times 233.01sq.inches \\ =466.02sqinches \end{gathered}$$

Hence, Total surface area of cylindrical tube is 466.02 sq. inches