Chapter 12, Problem 29SGR

To determine

To calculate:To find how many square inches of paper are needed to cover the gift

Answer to Problem 29SGR

  $298i{n}^2$ of paper are needed to cover the gift.

Explanation of Solution

Given information:Sarah is wrapping a gift that is $12$ inches long, $6$ inches wide and $4$ inches high

Formula Used:

Surface area of cuboid is given by the below formula:

  $Surfaceare{a}_{Cuboid}=2\left(Length\times Height\right)+2\left(Width\times Height\right)+2\left(Width\times Length\right)$

Calculation:

Given a gift that is $12$ inches long, $6$ inches wide and $4$ inches high

Here, dimensions of gift as follows:

  $\begin{array}{l}Length=12in.\\ Width=6in.\\ Height=4in.\end{array}$

Wrapping paper required to cover the gift is calculated by finding the total surface area of gift

Surface area is calculated as follows:

  $Surfaceare{a}_{Cuboid}=2\left(Length\times Height\right)+2\left(Width\times Height\right)+2\left(Width\times Length\right)$

Substituting the values, volume is

  $\begin{array}{l}Surfacearea=2\left(12\times 4\right)+2\left(6\times 4\right)+2\left(12\times 6\right)\\ Surfacearea=2\left(48\right)+2\left(24\right)++2\left(72\right)\\ Surfacearea=96+48+154\\ Surfacearea=298i{n}^2\end{array}$

Conclusion:

Hence, $298i{n}^2$ of paper are needed to cover the gift.