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balu736 [363]
3 years ago
9

The triangular prism has a volume of 27 cubic units.

Mathematics
2 answers:
Levart [38]3 years ago
8 0

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.

MariettaO [177]3 years ago
7 0

Answer:

9

Step-by-step explanation:

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

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