A cylindrical jar of radius 6 cm contains oil. Iron spheres each of ra

1.	A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimeters?
Answer» Given that, radius of cylindrical jar, r = 6 cm Depth/height of the jar, h = 2 cm Volume of the jar, V’ = πr² h ⇒ V’ = π (6)² (2) cm³ Radius of the sphere = 1.5 cm So, volume of the sphere = \(\frac{4}{3}πr^3\) = \(\frac{4}{3}π(1.5)^3\) Volume of oil in cylindrical jar = volume of n spheres needed to raise the level by 2 cm ∴ π (6)² (2) = \(n\times\frac{4}{3}π(1.5)^3\) ⇒ n = 16 ∴ number of iron sphere needed = 16

A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimeters?

Answer»

Given that,

radius of cylindrical jar, r = 6 cm

Depth/height of the jar, h = 2 cm

Volume of the jar, V’ = πr² h

⇒ V’ = π (6)² (2) cm³

Radius of the sphere = 1.5 cm

So,

volume of the sphere = \(\frac{4}{3}πr^3\)

= \(\frac{4}{3}π(1.5)^3\)

Volume of oil in cylindrical jar = volume of n spheres needed to raise the level by 2 cm

∴ π (6)² (2) = \(n\times\frac{4}{3}π(1.5)^3\)

⇒ n = 16

∴ number of iron sphere needed = 16