Oil is stored in a spherical vessel, occupying \frac{3}{4} of its full capacity. The radius of the spherical vessel is 28 cm. This oil is then poured into a cylindrical vessel with radius 21 cm. Find the height of the oil in the cylindrical vessel, correct to the nearest centimetre.
(Take π = \frac{22}{7})
Radius of the spherical vessel, r = 28 cm.
Volume of the spherical vessel = \frac{4}{3}\pi r^3
The oil occupies \frac{3}{4} of the vessel.
Volume of oil = \frac{3}{4}\times\frac{4}{3}\pi r^3
⇒ Volume of oil = πr³
⇒ Volume of oil = π × 28³ cm³
Radius of the cylindrical vessel, R = 21 cm.
Let the height of oil in the cylinder be h cm.
Volume of oil in the cylinder = πR²h
Equating the two volumes:
π × 28³ = π × 21² × h
⇒ 28³ = 21²h
⇒ h = \frac{28^3}{21^2}
⇒ h = \frac{21952}{441}
⇒ h ≈ 49.78 cm
Correct to the nearest centimetre, h = 50 cm.
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