#### Question

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.

#### Solution

Let us assume radius of cone=r.

Also, radius of cylinder=r.

And, height of cylinder=h.

Let` C_1` , be the curved surface area of cone

`∴ C_1=pirsqrt(r^2+h^2)`

Similarly,` C_2` be the curved surface area of cone cylinder.

`∴ C_2=2pirh`

According to question `C_2/C_1=8/5`

⇒ `(2pirh)/(pirsqrt(r^2+h^2))=8/5`

⇒ `10h=8sqrt(r^2+h^2)`

⇒ `100h^2=64r^2+64h^2`

⇒ `36h^2=64r^2`

`h/r=sqrt64/30`

⇒`(h/r)^2=64/36`

⇒` b/r=sqrt64/30=8/6=4/3`

`∴ r/h=3/4`

Is there an error in this question or solution?

Solution A Cylinder and a Cone Have Equal Radii of Their Bases and Equal Heights. If Their Curved Surface Areas Are in the Ratio 8:5, Show that the Radius of Each is to the Height of Each as 3:4. Concept: Surface Area of a Right Circular Cone.