Question

If the heights of two cones are in the ratio of 1 : 4 and the radii of their bases are in the ratio 4 : 1, then the ratio of their volumes is

Options

• 1 : 2

•  2 : 3

• 3 : 4

• 4 : 1

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume = `1/3 pir^2h`

Let the base radius and the height of the two cones be `r_1,h_1` and `r_2,h_2` respectively.

It is given that the ratio between the heights of the two cones is 1 : 4.

Since only the ratio is given, to use them in our equation we introduce a constant ‘k’.

So, `h_1` = 1k

`h_2`= 4k

It is also given that the ratio between the base radius of the two cones is 4 : 1.

Again, since only the ratio is given, to use them in our equation we introduce another constant ‘p’.

So, `r_1` = 4p

`r_2`= 1p

Substituting these values in the formula for volume of cone we get,

`(("Volume of cone_1")/("Volume of cone_2"))=((pi)(4p)(4p)(1k)(3))/((3)(pi)(1p)(1p)(4k))`

`= 4/1`