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

1 cubic unit

Explanation:

Answer 2

Option (2)

Explanation:

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

Factor of dilation of the sides of this prism (image) =
`(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

=
`((1)/(3))^3`

=
`(1)/(9)`

Now from the formula of volume scale factor,

`(1)/(9)=\frac{\text{Volume of image}}{\text{Volume of preimage}}`

`(1)/(9)=\frac{\text{Volume of image}}{27}`

Volume of the image prism =
`(27)/(9)` = 3 cubic units

Therefore, Option (2) will be the answer.