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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:

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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