Chapter ISG, Problem 8.1.2P

a.

To determine

To find total volume of each kind of box

Answer to Problem 8.1.2P

Volume of old box is 64 cubic units.

Volume of box is 88 cubic unit.

Explanation of Solution

Given information:

Volume of container= $x^3$

Volume of new container $x^3+2x^2-3x$

  $x=4$

Calculation:

Substituting values of x,

Volume of old box= ${(4)}^3$

Solving,

volume= $(4)\times (4)\times (4)$

Hence, volume of old box is 64 cubic units.

Volume of new box= ${(4)}^3+2{(4)}^2-3(4)$

Solving,

Volume=64+2(16)-12

So,

Volume= $64+36-12$

Hence, volume of box is 88 cubic unit.

b.

To determine

To find the difference between two

Answer to Problem 8.1.2P

Explanation of Solution

Given information:

Volume of container= $x^3$

Volume of new container= $x^3+2x^2-3x$

Calculation:

Difference= volume of new container-volume of old container.

Substituting values,

Difference= $x^3+2x^2-3x$ -( $x^3$ )

Solving,

= $2x^2-3x$

Hence, difference in volumes of both boxes area $2x^2-3x$