Chapter 11.5, Problem 13WE

To determine

To Find: How much dough will be needed for the $16-in$ pizza with the same thickness?

Answer to Problem 13WE

  $24oz$

Explanation of Solution

Given: If $16oz$ of dough are needed to make $8-in$ pizza.

Consider $8-in$ pizza

  $diameter=8$

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

Area of $8-in$ pizza.

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

Now consider $16-in$ pizza.

  $\begin{array}{l}r=\frac{d}{2}\\ r=\frac{16}{2}\\ r=8\end{array}$

Area of $16-in$ pizza.

  $\begin{array}{l}A=\pi r^2\\ $ A=\pi {(8)}^2$A=64\pi \end{array}$

Now let $x$ be the amount of dough needed to make a pizza with an area $1i{n}^2$

  $x=\frac{6}{16\pi }\mathrm{...}(i)$

Similarly

Let $y$ be the amount of dough needed to make a pizza with an area $64\pi$

  $\begin{array}{l}y=\frac{6}{16\pi }(64\pi )\\ y=24oz\end{array}$

Hence, $24oz$ is needed.