#### Question

The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.

#### Solution

Let ratio of radius be 'r '

Radius of `1^(st)`cone = 2r

Radius of `2^(nd)`cone = 3r

Similarly

Let volume ratio be ‘v’

Volume of `1^(st)` cone→ 4v

Similarly volume of `2^(nd)` cone → 5v

∴`V_1/V_2=(4v)/(5v)=4/5`

⇒ `(1/3pir_1^2h_1)/(1/3pir_1^2)=4/5`

⇒`( h_1(2r)^2)/(h_2(3r)^2)=4/5`

⇒` h_1/h_2xx(4r^2)/(9r^2)=4/5`

⇒ `h_1/h_2xx36/20=18/20=9/5`

∴ Ratio of the inner height is 9:5

Is there an error in this question or solution?

Solution The Ratio of Volumes of Two Cones Is 4 : 5 and the Ratio of the Radii of Their Bases is 2:3. Find The Ratio of Their Vertical Heights. Concept: Surface Area of a Right Circular Cone.