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Solution for 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. - CBSE Class 9 - Mathematics

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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?

APPEARS IN

 R.D. Sharma Mathematics for Class 9 by R D Sharma (2018-19 Session) (with solutions)
Chapter 18: Surface Areas and Volume of a Cuboid and Cube
Q: 23
Solution for 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. concept: Surface Area of a Right Circular Cone. For the course CBSE
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