# 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.

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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).