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RS Aggarwal Solutions Class 9 Mathematics Solutions for Volume And Surface Area Of Solids Exercise 15C in Chapter 15 - Volume And Surface Area Of Solids
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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 and height of each has the ratio 3:4.
ANSWER:
Consider the curved surface area of cylinder and cone as 8x and 5x.
So we get
2 πrh = 8x …….. (1)
Πr √ (h2 + r2) = 5x ……… (2)
By squaring equation (1)
(2 πrh) 2 = (8x) 2
So we get
4 π2r2h2 = 64 x2 …….. (3)
By squaring equation (2)
Π2r2 (h2 + r2) = 25x2 …… (4)
Dividing equation (3) by (4)
4 π2r2h2/ Π2r2 (h2 + r2) = 64 x2/25x2
On further calculation
h2/ (h2 + r2) = 16/25
It can be written as
9 h2 = 16 r2
So we get
r2/ h2 = 9/16
By taking square root
r/ h = ¾
We get
r: h = 3:4
Therefore, it is proved that the radius and height of each has the ratio 3:4.
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