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

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.