Question

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

Answer 1

$\frac{csa \: i}{csa \: ii} = \frac{\pi \times r \times l}{\pi \times r \times l} = \frac{3}{2}$
as diameter is equal so radius is also equal
now ratio comes out to be 3:2

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Answer 2

Hlo friend.. Cutiepie Here..

Here is ur answer:

Diameters of two right circular cones are equal.

Radius = Half of diameter.

It means radius of two right circular cones are equal.

Let the radius of Ist cone be r.

So, radius of IInd cone be r.

Slant height of these two circular cones are in ratio 3 : 2

Let the Slant height of Ist cone be 3 l

So,the Slant height of IInd cone be 2 l

Curved surface area of Ist cone

$\pi rl$

$= \pi r3l$

Curved surface area of IInd cone

$\pi rl$

$= \pi r2l$

Ratio of their curved surface area :

$= \frac{ Curved \: \: surface \: \: area \: \: of \: \: Ist \: \: cone \: \: }{Curved \: \: surface \: \: area \: \: of \: \: IInd \: \: cone }$

$= \frac{\pi r3l}{\pi r2l}$

$\pi \: \: and \: r \: cancel \: out$

$\frac{3l}{2l}$

$l \: \: cancel \: \: out$

$\frac{3}{2}$

Ratio of the curved surface area of these two right circular cone is 3 : 2.

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