The volume of a rectangular prism is 2,058 cubic cm. The length of the prism is 3 times the width. The height is twice the width. Find the length of the prism.

Let the height of prism be

H

.

As it is twice the width, width is

H

2

.

Length being

3

times width should be

3

*

H

2

=

3

H

2

Hence, volume is

3

H

2

*

H

*

H

2

=

3

4

H

3

, but it is

2058

cubic cm.

Therefore

3

4

H

3

=

2058

and

H

3

=

2058

*

4

3

=

686

2058

*

4

1

3

or

H

3

=

2

*

2

*

2

*

7

*

7

*

7

Hence

H

=

2

*

7

=

14

Height of the prism is

14

cm.