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WBBSEClass 10MathematicsRight Circular Cylinder02 Mark2022 Moderate

QQuestion

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.

Exam-ready answer • 02 Mark

Answer

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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