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 needed to raise the level of the oil by two centimeters?

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Q.

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 needed to raise the level of the oil by two centimeters?

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a

16

b

32

c

17

d

37

answer is A.

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Detailed Solution

Given,
Cylindrical jar radius=6cm,
Iron sphere radius=1.5cm.
We need to find, spheres needed to raise the level of the oil by two centimeters.

⇒

Volume of the cylinder = n × Volume of a sphere
We know that,
Volume of the sphere

= 43 π r 3

.
Volume of the cylinder

= π r 2 h

.
Substituting the values,

π × 6 × 6 × 2 = n × 43 π × (1.5) 3 n = 6 × 6 × 2 × 3 4 × (1.5) 3 n = 16

The number of spheres required to raise the level of the oil by 2cm = 16.
Therefore, the correct option is 1.

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