Question

the ratio of the height of two right circular cones is 5:2 and that of their base radii is 2:5.Find the ratio of their volumes.
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Answer 1

Solution :-

Let us assume that,

• Radius of first cone = r1 = 2x .
• Radius of second cone = r2 = 5x .
• Height of first cone = h1 = 5y .
• Height of second cone = h2 = 2y .

we know that,

• Volume of cone = (1/3) * π * (radius)² * height .

So,

→ Volume of 1st cone : Volume of 2nd cone = (1/3) * π * (r1)² * h1 = (1/3) * π * (r2)² * h²

→ V1 : V2 = (1/3) * π * (2x)² * 5y : (1/3) * π * (5x)² * 2y

→ V1 : V2 = 4x² * 5y : 25x² * 2y

→ V1 : V2 = 20x²y : 50x²y

→ V1 : V2 = 2 : 5 .

Hence, the ratio of their volumes is 2 : 5 .

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