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# 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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ConceptSurface Area of a Right Circular Cone

#### 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

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 20: Surface Areas and Volume of A Right Circular Cone
Ex.20.10 | Q: 19 | Page no. 8
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.
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