Question

The diameter of the two right circular cones are equal if their slant heights are in the
ratio 3 :2, then what is the ratio of their curved surface areas?

Answer 1

LET DIAMETER =?
LET THE SLANT HEIGHT BE =3XAND 2X
C.S.A=πRL
πR×3X
C.S.A=πRL
πR×2X
C.S.A /C.S.A =πR×3X/πR×2X
=3/2

Answer 2

Answer:

$Ratio \: of \: curved \: surface \: area \\=\frac{3}{2}$

Step-by-step explanation:

Let equal diameter of the two right circular cones = d

Therefore, radii of two circular cones = r

$Let \: l_{1}\: and \: l_{2} \: are\\ slant \: heights \: of \: two \\ cones \: respectively$

$Ratio \: of \: slant \: heights \\=\frac{l_{1}}{l_{2}}=\frac{3}{2}\: (given)$

$Now,\\Ratio \: of \: curved \: surface \: area \\=\frac{\pi rl_{1}}{\pi rl_{2}}\\=\frac{l_{1}}{l_{2}}\\=\frac{3}{2}$

Therefore,

$Now,\\Ratio \: of \: curved \: surface \: area \\=\frac{3}{2}$

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