If the height of two right circular cylinders is in the ratio of 1 : 2, and the perimeters of the base are in the ratio of 3 : 4, find the ratio of their volumes.
WBBSE
Class X
Mathematics
Right Circular Cylinder
02 Mark
2022
h1 : h2 = 1 : 2 — (i)
Perimeters of the base = 3 : 4
C1 : C2 = 3 : 4
or, 2πr1 : 2πr2 = 3 : 4
or, r1 : r2 = 3 : 4 — (ii)
Ratio of their volumes = V1 : V2
= πr1²h1 : πr2²h2
= r1²h1 : r2²h2
= {r_1}²\over {r_1}² × {h_1}\over {h_2}
= ({3\over 4})² × {1\over 2}
= {9\over 16} × {1\over 2}
= 9 : 32
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