Chapter 11.5, Problem 14WE

To determine

To Find: The diameter.

Answer to Problem 14WE

  $11.312in$

Explanation of Solution

Given: one can of pumpkin pie mix will make a pie of diameter $8in$ . If two cans of pie mix are used to make a larger pie of the same thickness.

  $diameter=8$

  $\begin{array}{l}r=\frac{d}{2}\\ r=\frac{8}{2}\\ r=4\end{array}$

Area of $8in$ pie of 1 can.

  $\begin{array}{l}A=\pi r^2\\ $ A=\pi {(4)}^2$A=16\pi \mathrm{..}(i)\end{array}$

Now consider $x$ be the diameter of two cans..

  $\begin{array}{l}A=\pi r^2\\ $ A=\pi {(\frac{x}{2})}^2$A=\frac{\pi x^2}{4}\mathrm{...}(ii)\end{array}$

From $(i)and(ii)$

  $\begin{array}{l}{\left(\frac{8}{x}\right)}^2=\left(\frac{1}{2}\right)\\ x=8\sqrt{2}\\ x=8(1.414)\\ x=11.312in\end{array}$

Hence, diameter is $11.312in$ .