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:
1 cubic unit
Step-by-step explanation:
We are given that
Volume of triangular prism[tex]V_1[/tex]= 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
[tex]V_2=k^3V_1[/tex]
Where [tex]k=[/tex] scale factor
[tex]V_2[/tex]= Volume of triangular prism after applying the scale factor on each side
[tex]V_1[/tex]=Original volume of triangular prism
Substitute the values then we get
[tex]V_2=(\frac{1}{3})^3(27)==1[/tex] cubic unit
Answer: 1 cubic unit
