Question

1. Jewelry box has a volume of 240 cubic inches. Its height is 12 inches, its width x ininches, and its length (x + 8) inches.a. Draw and label a diagram of the jewelry box.b. Write an equation for the volume of the box. Write your answer in standard form.c. Find the width of the box in meters.

Answer 1

A) The above figure is the label diagram of the jewelry box.

B) The equation of the volume will be,

$\begin{gathered} \text{Volume of a cuboid=length}\times width\times height \\ \text{length}=(x+8) \\ \text{width}=x \\ \text{height}=12\text{inches} \end{gathered}$$\begin{gathered} \text{Volume}=(x+8)(x)(12)in^3 \\ =12(x^2+8x)=(12x^2+96x)in^3 \end{gathered}$

The equation for the volume of the box is (12x²+96x)in³.

C) To solve for the width of the box in metres, we will equate the equation of the volume to 240in³,

$\begin{gathered} 12x^2+96x^{}=240 \\ \text{collect like terms} \\ 12x^2_{}+96x-240=0 \\ \text{Divide through by 12} \\ \frac{12x^2}{12}+\frac{96x}{12}-\frac{240}{12}=0 \\ x^2+8x-20=0 \\ \end{gathered}$$\begin{gathered} x^2+10x-2x-20=0 \\ x(x+10)-2(x+10)=0 \\ (x-2)(x+10)=0 \\ x-2=0\text{ or x+10=0} \\ x=2\text{ or x=-10} \end{gathered}$

The width can never be negative, therefore the width is 2in.

Finally let us now convert the width to meters,

$\begin{gathered} 1\text{inch}=0.0254\text{metres} \\ 2\text{inches}=2\times0.0254metres \\ =0.0508metres \end{gathered}$

Hence, the width is 0.0508metres.