Question

Two cones with radii and heights are a,b and b,a respectively then find the ratio of volumes and ratio of the LSA's of cones.

Answer 1

ratio of volumes
1/3πa*a*b : 1/3πb*b*a
after cancelling,
a. : b
ratio of lsa
slant height , l = √a*a+b*b for both cones
ratio = πal : πbl = a:b
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Answer 2

HELLO DEAR,

GIVEN THAT;-

---------1ST CONE -----

height = b , radius = a

slant height (l)
$\sqrt{ {a}^{2} + {b}^{2} }$

------2nd cone-------

height = a radius = b

slant height (L)
$\sqrt{ {b}^{2} + {a}^{2} }$

hence, slant height of both cone are same l=L

=
$\sqrt{ {b}^{2} + {a}^{2} }$

---(1)

ratio of there voulme

=>
$\frac{ \frac{1}{3} \pi {a}^{2} b}{ \frac{1}{3}\pi {b}^{2} a} \\ \\ = \frac{a}{b} \\ \\ = a :b$
------(2)

and the ratio of there L.S.A

=>
$\frac{\pi al}{\pi b L} \\ \\ \frac{a}{b} = a:b$
I HOPE ITS HELP YOU DEAR,
THANKS