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Question
The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is
Options
1 : 2 : 3
2 : 1 : 3
1 : 3 : 2
3 : 1 : 2
Solution
3 : 1 : 2
Explanation;
Hint:
Volume of (cylinder : cone : sphere)
= `pi"r"^2"h" : 1/3 pi"r"^2"h": 4/3 pi"r^3`
(DIvidend by πr2) = `"h" : "h"/3 : (4"r")/3`
But r = `"h"/2 = "h" : "h"/3 : (4 xx "h")/(3 xx2)`
= `"h" : "h"/3 : (2"h")/3`
= 3 : 1 : 2
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