A cylindrical vessel of height 10 cm has base radius 60 cm If d is the diameter of a spherical vesse...........

Quantitative Aptitude ( CCS) Mensuration 3D

A cylindrical vessel of height 10 cm has base radius 60 cm. If d is the diameter of a spherical vessel of equal volume, then what is d equal to ?

30 cm

60 cm

90 cm

120 cm

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Explanation:

Given, height of cylindrical vessel (h) = 10 cm and radius of cylindrical vessel (r₁) = 60 cm
And, Diameter of spherical vessel = d
∴ Radius of spherical vessel (r₂) = d/2
By given condition,
Volume of cylindrical vessel = volume of spherical vessel
∴ πr₁²h = 4/3πr₂³
⇒ (60)² × 10 = 4/3(d/2)³
⇒ d³ = 216000
∴ d = 60 cm