Question

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

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

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