Question

The triangular prism has a volume of 27 cubic units.

Answer 1

Given:

The volume of the triangular prism = 27 cubic units

To find the volume of the prism if each side is dilated by $\frac{1}{3}$

Formula

The volume of a triangular prism

$V = \frac{1}{2} ach$

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,

$a \rightarrow \frac{1}{3} a$

$c \rightarrow \frac{1}{3} c$ and

$h \rightarrow \frac{1}{3} h$

So,

After dilation the volume will be

$V_{1} =\frac{1}{2} (\frac{a}{3} )(\frac{c}{3} )(\frac{h}{3} )$

or, $V_{1} =\frac{1}{9} (\frac{1}{2} ach)$

or, $V_{1}=\frac{1}{9} (27)$ [Since, $V = \frac{1}{2} ach = 27$]

or, $V_{1} = 3$

Hence,

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

Answer 2

Answer:

9

Step-by-step explanation:

27 x $\frac{1}{3}$=9