Quantity I.
Height of cylinder = (23)2 = 64 cm
Let the radius of the cylinder be 'R1' cm and the radius of the sphere be 'R2' cm.
The volume of a Cylinder/ the volume of a sphere = 75/28
∏R12h/ (4/3 * ∏R23) = 75/28
3 * R12 * 64/ 4 * R23 = 75/28
R1 = 5/8 * √(R23/7) ............... eq (i)
The curved surface area of a cylinder = 14080 cm2
2∏R1h = 14080 cm2
2 * 22/7 * R1 * 64 = 14080
R1 = 35 cm ........................eq (ii)
From eq (i) and (ii)
5/8 * √(R23/7) = 35
R23 = 56 * 56 * 7
R2 = 28 cm
Quantity II.
Let the radius of the cone be 'R'.
The curved surface area of a cone/ the curved surface area of a hemisphere = 15/8
∏r l/ 2∏r2 = 15/8
R * 35/ (2 * 14 * 14)= 15/8
R = 21 cm
The required value = 21 * 4/3 = 28 cm
Hence, Quantity I ≥ Quantity II.
Study Notes
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