Chapter 12.8, Problem 4GP

To determine

To find : Amount of cardboard needed to make a box for a single slice of pizza.

Answer to Problem 4GP

  $116\text{in}{.}^2$

Explanation of Solution

Given information :

The given information is, the box is shown in the shape of triangular prism for a single slice of pizza.

  

Formula Used:

Area of triangle = $\frac{1}{2}\times b\times h$

Area of rectangle = $l\times B$

Calculation :

Surface area of cardboard = $2$ (Area of triangle) + $2$ (Area of rectangle) + (Area of rectangle)

Area of triangle = $\frac{1}{2}\times 7\times 12=42\text{in}{.}^2$

Area of rectangle = $1\times 12.5=12.5\text{in}{\text{.}}^{\text{2}}$

Area of rectangle = $1\times 7=7\text{ in}{\text{.}}^{\text{2}}$

Total Surface area = $2(42)+2(12.5)+7$

  $\begin{array}{l}=84+25+7\\ =116\text{in}{\text{.}}^2\end{array}$

Total required amount of cardboard is $116\text{in}{\text{.}}^2$ .