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.

Answer 1

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`