Question

Which of the two solids below are similar ?

A. I and II
B. I and II
C. II and II
D. I, II and I
E. None of the solids are similar.

Answer 1

Answer: I and II.

Explanation:

By definition, two solids are similar if their corresponding sides are in the same ratio.

Knowing this, let's find which solids are similar:

Corresponding sides ratio of solids I and II:

`(3)/(2)=(2)/((4)/(3))=(5)/((10)/(3))`

`(3)/(2)=(3)/(2)=(3)/(2)`

Corresponding sides ratio of solids I and III:

`(3)/((9)/(2))=(2)/(3)=(5)/(8)`

`(2)/(3)=(2)/(3)=(5)/(8)`

Corresponding sides ratio of solids II and III:

`(2)/((9)/(2))=((4)/(3))/(3)}=((10)/(3))/(8)}`

`(4)/(9)=(4)/(9)=(5)/(12)`

You can observe that the solids I and II are similar.