Question

the base radii of two right circular cones of the same height are in the ratio 3:5. find the ratio of their volumes

Answer 1

Solution :-

Let there be cone 1 and cone 2 respectively.

Let the r and R be the radii of the two right circular cones respectively.

Ratio of base radii = 3 : 5

Volume of cone = 1/3πr²h

⇒Volume of cone 1/Volume of cone 2

⇒ (1/3*πr²h)/(1/3πR²h)

⇒ (1/3*π*3²*h)/(1/3*π*5²*h)

= 3²/5²

= 9/25

= 9 : 25

So, the ratio of their volumes is 9 : 25

Answer.

Answer 2

Let the volume two cones be v1 & v2 & r1 and r2 be the radii of the two right circular cones & height of the two cones be h.

Ratio of base radii = r1:r2= 3 : 5

Volume of cone = 1/3πr²h

Volume of first cone (v1)1/Volume of second cone (v2)

=(1/3×π×r1²×h)/(1/3×π×r2²×h)

= (1/3×π×3²×h)/(1/3×π×5²×h)

= r1²/r2²

= 3²/5²

= 9/25

= 9 : 25

Hence, the ratio of their volumes is 9 : 25

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