A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3 : 1.
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Given : A cylinder and a cone are having equal radii of their bases and heights.
Let, the radius of the cone and radius of the cylinder be r and Height of the cone and height of the cylinder be h.
Now,
Volume of Cylinder (V1) / Volume of cone (V2) = πr²h/(1/3 πr²h)
V1/V2 = 1/(⅓)
V1/V2 = 1 × 3/1
V1/V2 = 3/1
V1 : V2 = 3 : 1
Hence, it is proved that their volumes are in the ratio 3 : 1.
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