Chapter 12, Problem 9STP

To determine

To calculate:To find which pipe has greater outer surface area

Answer to Problem 9STP

Outer surface area of both the pipes are same

Explanation of Solution

Given information:A plumber has two drainpipes shaped like cylinders. The first pipe is $8$ inches long and has a diameter of $1.25$ inches. The second pipe is $10$ inches long and has a diameter of $1$ inch

Formula Used:

Outer surface area of cylinder is given as follows:

Outer Surface Area $=2\pi rh$

Where,

  $r=$ Radius

  $h=$ Height

Calculation:

The first pipe is $8$ inches long and has a diameter of $1.25$ inches.

Thus, dimensions of first pipe are

  $Radius=\frac{Diameter}{2}=\frac{1.25}{2}=0.625in$

  $Height=8in$

Outer surface area of first pipe is

  $\begin{array}{l}Are{a}_1=2\times \frac{22}{7}\times 0.625\times 8\\ Are{a}_1=31.428i{n}^2\end{array}$

The second pipe is $10$ inches long and has a diameter of $1$ inch

Thus, dimensions of first pipe are

  $Radius=\frac{Diameter}{2}=\frac{1}{2}=0.5in$

  $Height=10in$

Outer surface area of first pipe is

  $\begin{array}{l}Are{a}_2=2\times \frac{22}{7}\times 0.5\times 10\\ Are{a}_2=31.428i{n}^2\end{array}$

On comparing the outer surface areas of Pipe1 and Pipe2, Outer surface area of both the pipes are same

Conclusion:

Hence,Outer surface area of both the pipes are same