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Nesterboy [21]
3 years ago
8

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 di

lated by a factor One-third? 1 cubic unit 3 cubic units 8 cubic units 9 cubic units
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
4 0

Answer:

Option (2)

Step-by-step explanation:

Volume of a prism A (preimage) = 27 cubic units

Factor of dilation of the sides of this prism (image) = \frac{1}{3}

Volume scale factor of these prisms = \frac{\text{Volume of image}}{\text{Volume of preimage}}

Since, Volume scale factor = (Scale factor of dilation of the sides)³

                                             = (\frac{1}{3})^3

                                             = \frac{1}{9}

Now from the formula of volume scale factor,

\frac{1}{9}=\frac{\text{Volume of image}}{\text{Volume of preimage}}

\frac{1}{9}=\frac{\text{Volume of image}}{27}

Volume of the image prism = \frac{27}{9} = 3 cubic units

Therefore, Option (2) will be the answer.                                                    

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