Chapter 4.3, Problem 54IP

a.

To determine

To find: the missing components of table.

Answer to Problem 54IP

Side length(units)	Area of square (units square)	Volume of cube (unit cube)
s	$s^2$	$s^3$
2s	$4s^2$	$8s^3$
3s	$9s^2$	$27s^6$
$s^2$	$s^4$	$s^6$
$s^3$	$s^6$	$s^9$

Explanation of Solution

Given information:

Side length(units)	Area of square (units square)	Volume of cube (unit cube)
s	$s^2$	$s^3$
2s
3s
$s^2$
$s^3$

Calculation : to find the missing elements, multiply and simplify,

Side length(units)	Area of square (units square)	Volume of cube (unit cube)
s	$s^2$	$s^3$
2s	$4s^2$	$8s^3$
3s	$9s^2$	$27s^6$
$s^2$	$s^4$	$s^6$
$s^3$	$s^6$	$s^9$

b.

To determine

To state: that how the area and volume affected if the side length is doubles and tripled.

Answer to Problem 54IP

When the side length is double the area increases the $4$ times and volume increases $8$ times and when the side length is tripled the area increases the $9$ times and the volume increases $27$ times.

Explanation of Solution

Given information:

Side length(units)	Area of square (units square)	Volume of cube (unit cube)
s	$s^2$	$s^3$
2s
3s
$s^2$
$s^3$

to find the missing elements, multiply and simplify,

Side length(units)	Area of square (units square)	Volume of cube (unit cube)
s	$s^2$	$s^3$
2s	$4s^2$	$8s^3$
3s	$9s^2$	$27s^6$
$s^2$	$s^4$	$s^6$
$s^3$	$s^6$	$s^9$

From the above table it can be observed that When the side length is double the area increases the $4$ times and volume increases $8$ times and when the side length is tripled the area increases the $9$ times and the volume increases $27$ times.

c.

To determine

To state: that how the area and volume affected if the side length is squared and cubed.

Answer to Problem 54IP

When the side length is squared the area also squared and volume also squared and when the side length is cubed the area cubedand the volume cubed.

Explanation of Solution

Given information:

Side length(units)	Area of square (units square)	Volume of cube (unit cube)
s	$s^2$	$s^3$
2s
3s
$s^2$
$s^3$

to find the missing elements, multiply and simplify,

Side length(units)	Area of square (units square)	Volume of cube (unit cube)
s	$s^2$	$s^3$
2s	$4s^2$	$8s^3$
3s	$9s^2$	$27s^6$
$s^2$	$s^4$	$s^6$
$s^3$	$s^6$	$s^9$

From the above table it can be observed that When the side length is squared the area also squared and volume also squared and when the side length is cubed the area cubed and the volume cubed.