Chapter 12, Problem 7STP

To determine

To calculate:To find how much wrapping paper would Nicole needed to completely cover the gift box

Answer to Problem 7STP

The amount of wrapping paper needed to completely cover the gift box is $864i{n}^2$

Explanation of Solution

Given information:Gift box is

Formula Used:

Surface area of cuboid is given as

  $SA=2\left(lw+wh+lh\right)$

Where,

  $SA=$ Surface Area

  $l=$ Length

  $w=$ Width

  $h=$ Height

Calculation:

Amount of wrapping paper needed to completely cover the gift box is equal to surface area of the gift box.

Here, shape of gift box is cuboid

Given dimensions of cuboid are as follows:

  $\begin{array}{l}Length=18in.\\ Width=10in.\\ Height=9in.\end{array}$

Surface area of cuboid is calculated as

  $SA=2\left(lw+wh+lh\right)$

Substituting the values,

  $\begin{array}{l}SA=2\left(\left(18\right)\left(10\right)+\left(10\right)\left(9\right)+\left(18\right)\left(9\right)\right)\\ SA=2\left(180+90+162\right)\\ SA=2\left(432\right)\\ SA=864\end{array}$

Conclusion:

Hence, amount of wrapping paper needed to completely cover the gift box is $864i{n}^2$

Thus, correct option is D