Question

The triangular prism has a volume of 27 cubic units.

What will be the volume of the prism if each side is dilated by a factor 1/3
1 cubic unit, 3,8,9

Answer 1

1 cubic unit

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=((1)/(3))^3(27)==1` cubic unit

Answer: 1 cubic unit

Answer 2

1 cubic unit will be the volume of the prism.

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