Question

The triangular prism has a volume of 27 cubic units.

Answer 1

Answer:

1 cubic unit will be the volume of the prism.

Step-by-step explanation:

Volume of the triangular prism = 27 cubic units

Since formula of volume of the triangular prism = (1/3)A×h

27 = (1/3)A×h ⇒ Ah = 27×3 = 81

Now each side of the prism is dilated then we have to calculate the volume of new prism.

V' = (1/3)×A'×h'

= (1/3) (1/9)A×(1/3)h = (1/81)×Ah = (1/81)×81 = 1 cubic unit

Therefore the volume of new prism will be 1 cubic unit

Answer 2

Answer:

1 cubic unit

Step-by-step explanation:

We are given that

Volume of triangular prism$V_1$= 27 cubic units

We are given that each side of triangular prism dilated by a factor of  1/3.

We have to find the new volume of triangular prism.

We have a relationship between the volumes

$V_2=k^3V_1$

Where $k=$ scale factor

$V_2$= Volume of triangular prism after applying  the scale factor on each side

$V_1$=Original volume of triangular prism

Substitute the values then we get

$V_2=(\frac{1}{3})^3(27)==1$ cubic unit

Answer: 1 cubic unit