Question

The two cones below are similar. What is the height of the smaller one?

Answer 1

D.
`(20)/(7)`

Explanation:

When two solid same type figures are similar then their corresponding measures are in same proportion,

i.e. if a cone having radius
`r_1` and height
`h_1` is similar to the cone having radius
`r_2` and height
`h_2`.

Then,

`(r_1)/(r_2)=(h_1)/(h_2)`

Here,

`r_1=7, r_2=4, h_1 = 5, h_2 = x`

By substituting the values,

`(7)/(4)=(5)/(x)`

`7x = 20`

`\implies x = (20)/(7)`

Hence, the height of smaller one is 20/7 units.

Answer 2

D. 20/7

Explanation:

Since

4/7 = x/5

Multiply the left side by x and the right side by 4 as shown below

7*x = 4*5

7x = 20

Then dividing both sides by 7 would cancel on the left

7x/7=x

X = 20/7