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Chapter 8: Q7. (page 520)

A rectangular gift box has dimensions that can be represented as shown in the figure. The volume of the box is 672 cubic inches. Which of the following is not a dimension of the box?

A 6 in.

B 7 in.

C 8 in.

D 12 in.

Short Answer

Expert verified

6 in. is not a dimension of the box.

Step by step solution

01

Step 1. Write the formula of volume of rectangular box.

Let l, band h be the length, width and height of the rectangular gift box respectively.

Volume of a rectangular box is

V=l脳b脳h

02

Step 2. Apply formula of volume of rectangular box.

Replace V with 672, w with l, b withw鈭�5 and h with w鈭�4.

ww鈭�5w鈭�4=672w3鈭�4w2鈭�5w2+20w=672w3鈭�9w2+20w鈭�672=0

03

Step 3. Find the dimensions of the rectangular box.

By solving the above equation, w=12.

Replace w by 12 in b=w鈭�5.

b=w鈭�5=12鈭�5=7in

Replace w by 12 in h=w鈭�4.

h=w鈭�4=12鈭�4=8in

The dimensions of the rectangular box are 12 in, 7 in and 8 in. 6 in is not the dimension of the rectangular box. Therefore, option A is the required answer.

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