Question

If $6$ oz of dough is needed to make an $8$ inches Pizza, how much dough will be needed to make an $16$ inches Pizza of the same thickness? (Hint: Compare the areas of the Pizza tops.)

Answer 1

Step- 1: The area of the $8$ inches Pizza:

The diameter of the Pizza is $8$ inches. Then, the radius will be $4$ inches.

The area of the circular Pizza with radius $4$ unit is calculated as:

$\begin{array}{rcl}{A}_1& =& \pi {\left(4\right)}^2\\ & \Rightarrow & A_1=16\pi \end{array}$

Step- 2: The area of the $16$ inches Pizza:

The diameter of the Pizza is $16$ inches. Then, the radius will be $8$ inches.

The area of the circular Pizza with radius $8$ unit is calculated as:

$\begin{array}{rcl}{A}_2& =& \pi {\left(8\right)}^2\\ & \Rightarrow & A_2=64\pi \end{array}$

Step- 3: The amount of dough required:

$\begin{array}{rcl}16\mathrm{\pi }{\mathrm{in}}^2& =& 6\mathrm{oz}\\ 1{\mathrm{in}}^2& =& \frac{6}{16\mathrm{\pi }}\mathrm{oz}\\ 64\mathrm{\pi }{\mathrm{in}}^2& =& \frac{6}{16\mathrm{\pi }}\times 64\mathrm{\pi }\mathrm{oz}\\ 64\mathrm{\pi }{\mathrm{in}}^2& =& 6\times 4\mathrm{oz}\\ 64\mathrm{\pi }{\mathrm{in}}^2& =& 24\mathrm{oz}\end{array}$

Hence, $\mathbf{24}$ oz of dough will be needed to make $16$ inches of Pizza.