Question

There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former.Find the ratio of their radii.

Plz explain in detail with all required steps…

Points : 20 ☺

Answer 1

let r1 , l1 is the radius , slant height of first cone and r2 , l2 is the radius and slant height of 2nd cone respectively .

now,
according to question ,
surface area of 1st cone = 2 x surface area of 2nd cone

pi.r1. l1 = 2 xpi. r2. l2
r1. l1 =2 r2 .l2

r1 /r2 = 2l2/l1 ----------(1)

we have required to value of l2/l1 for finding r1 /r2 value
so, we read next sentence in question .

again ,
slant height of latter = 2 slant height of former
it means
l2 = 2 l1
l2/l1 = 2

put this equation (1)
r1. l1 = 2r2. l 2
r1/r2 =2 (l2/l1)=2 x 2

hence ratio of radius is 4 : 1

Answer 2

Hope this helps.....

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