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Volume of a cone
1) If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their height is:
25 : 65
16 : 64
25 : 64
25 : 50
1/10
Solution
Answer:
25 : 64
Explanation:
Since the diameters are in the ratio 4 : 5, it follows that their radii are in the ratio 4 : 5
Let them be 4r and 5r
Let the height be h and H
Ratio of volumes = (1/3π × (4r)² × h / 1/3π × (5r)² × H)
= (16h / 25H)
(16h / 25H)
= 1/4 or h/H
= (1/4 × 25/16)
= 25 / 64
= 25 : 64 cm³
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