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प्रश्न
The heights of two cones are in the ratio 1:3 and their base radii are in the ratio 3:1. Find the ratio of their volumes.
उत्तर
Let radius of first cone be 3r and height be h, then radius of second cone will be rand height will be 3h.
Volume of cone = `1/3 xx (pir^2) xx h`
Ratio of volumes of cone = `"Volume of first cone"/"Volume of second cone"`
= `(1/3 xx (pi(3r)^2) xx h)/(1/3 xx (pir^2) xx 3h)`
= `(1/3 pi9r^2h)/(1/3pir^2 3h)`
= `3/1`
Ratio of volumes of cone = 3:1
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