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Q.

A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm.

Then, the radius of the ball should be 9 cm.

State true or false.

see full answer

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a

True

b

False

answer is A.

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Detailed Solution

Given, radius of cylinder = 12 cm,
It is also given that a spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm.

⇒

Volume of water displaced = volume of spherical ball…..(i)
And, height of water raised =6.5cm.
We know that,
Volume of the sphere i.e., spherical ball

= 43 π r 3

.
Volume of the cylinder i.e., water displaced

= π r 2 h

.
Substituting the values in eq(i),

π r 2 h = 43 π r 3 π × (12) 2 × 6.75 = 43 π r 3 12 × 12 × 6.75 × 34 = r 3 r 3 = 729 r = 9

.
The radius of the ball is 9cm.
Therefore, the given statement, “the radius of the ball should be 9 cm” is true.

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