Chapter 9.4, Problem 24E

a.

To determine

To find expression of the volume of the glass case.

Answer to Problem 24E

  $x^2-8x-768=0$

Explanation of Solution

Given information:

Volume of the glass case is $768c{m}^3$

Length( l) of case is $(x-8)cm$

Width( b ) of case is $(x)cm$

Depth( h ) of case is 1 centimeter

Formula used:

Volume of the glass case, $V=lbh$

Calculation:

Volume of the glass case $=768$

Length( l) of glass case $=x-8$

Width( b ) of glass case $=x$

Depth( h ) of case $=1$

Using formula

  $768=(x-8)\times x\times 1$

On solving

  $768=x^2-8x$

On solving

  $x^2-8x-768=0$

b.

To determine

To calculate dimensions of the glass case.

Answer to Problem 24E

Width( b ) of case $\text{=32 }cm$

Length( l) of glass case $=24cm$

Depth( h ) of case $=1cm$

Explanation of Solution

Given information:

Volume of the glass case is $768c{m}^3$

Length( l) of case is $(x-8)cm$

Width( b ) of case is $(x)cm$

Depth( h ) of case is 1 centimeter

Formula used:

Volume of the glass case, $V=lbh$

Calculation:

Volume of the glass case $=768$

Length( l) of glass case $=x-8$

Width( b ) of glass case $=x$

Depth( h ) of case $=1$

Using formula

  $768=(x-8)\times x\times 1$

On solving

  $768=x^2-8x$

On solving

  $x^2-8x-768=0$

On solving

  $x^2+24x-32x-768=0$

On solving

  $x(x+24)-32(x+24)=0$

On solving

  $(x+24)(x-32)=0$

On solving

  $(x+24)=0$

  $(x-32)=0$

On solving

  $x=-24$

  $x=32$

width cannot be negative

Then

Width( b ) of case $\text{=32 }cm$

Length( l) of glass case $=24cm$

Depth( h ) of case $=1cm$