Question

the radius and slant height of a cone are in the ratio of 3:5 . IF its curved surface area is 2310 cm2, find its radius , height and slant height.

Answer 1

given that
CSA of the cone = 2310
r:l = 3:5
r/l = 3/5
3l = 5r  -------------------------(1)
CSA of cone = 2310
πrl = 2310
rl = 2310×7/22
rl = 735
l = 735/r --------------------(2)
from (1) and (2)
3(735/r) = 5r
2205/r = 5r
2205 = 5r²
r² = 441
r = 21 cm    (proved)
from (1)
3l = 5(21)
3l = 105
l = 35 cm   (proved)

we have on relation between r, h , l.
l = √r²+h²
then
h = √l²-r²
h = √ (35)² - (21)²
h = √1225 - 441
h = √784
h = 28 cm    (proved).

Answer 2

Answer : I think correct answer is

let radius = 3x and slant height = 5x

given that C.S.A. is 2310 but,

csa of cone = π*r*l

therefore , 2310= 22/7 * 3x * 5x

2310= 330x² / 7

2310*7/330 = x²

49 = x²

x = 7 ( as underroot of 49 is 7 )

So , we have got the answer in this manner.

And to find height use formula l^2 =underroot ( h^2 + r^2 )

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