Question

The triangular prism has a volume of 27 cubic units.

A triangular prism.
What will be the volume of the prism if each side is dilated by a factor One-third?
1 cubic unit
3 cubic units
8 cubic units
9 cubic units

Answer 1

9

Explanation:

27 x
`(1)/(3)`=9

Answer 2

Given:

The volume of the triangular prism = 27 cubic units

To find the volume of the prism if each side is dilated by
`(1)/(3)`

Formula

The volume of a triangular prism

`V = (1)/(2) ach`

where, a be the height of the triangle

c be the base of the triangle

h be the height of the prism

Let us take after dilation the we get,

`a \rightarrow (1)/(3) a`

`c \rightarrow (1)/(3) c` and

`h \rightarrow (1)/(3) h`

So,

After dilation the volume will be

`V_(1) =(1)/(2) ((a)/(3) )((c)/(3) )((h)/(3) )`

or,
`V_(1) =(1)/(9) ((1)/(2) ach)`

or,
`V_(1)=(1)/(9) (27)` [Since,
`V = (1)/(2) ach = 27`]

or,
`V_(1) = 3`

Hence,

After dilation the volume of the prism will be 3 cubic unit.