Question

Jake was rewriting the equation for the Surface Area of acylinder so that it was solved for "h." His friend Niki noticed thathe made an error and explained it to Jake. What error did Nikipoint out to Jake if she was correct that he made a mistake? *

Answer 1

Given

Jake rewrote the equation of the surface area of a Cylinder as it is solved for h as it is shown in the figure.

To find the error made by Jake.

Now,

The surface area of the cylinder is given by,

`\begin{gathered} \text{Surface area}=2\pi r(h+r) \\ A=2\pi r^2+2\pi rh \end{gathered}`

Subtracting both sides with

`2\pi r^2`

Implies,

`\begin{gathered} A-2\pi r^2=2\pi r^2-2\pi r^2+2\pi rh \\ A-2\pi r^2=2\pi rh \end{gathered}`

Dividing both sides by

`2\pi r`

gives,

`\begin{gathered} (A-2\pi r^2)/(2\pi r)=(2\pi rh)/(2\pi r) \\ (A)/(2\pi r)-(2\pi r^2)/(2\pi r)=h \\ (A)/(2\pi r)-r=h \end{gathered}`

Comparing the above solution for h and the solution of h in the figure, we get the error in the last step as Jake didn't simplify the left side correctly.

Hence, the error is c) On the last step, Jake didn't simplify the left side correctly.