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# A Cylinder of Radius 12 Cm Contains Water to a Depth of 20 Cm. a Spherical Iron Ball is Dropped into Cylinder and Thus the Level of Water Raised by 6.75 Cm. Find Radius of the Ball. (Use 𝜋 = 22/7). - CBSE Class 9 - Mathematics

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ConceptVolume of a Sphere

#### Question

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. Find the radius of the ball.
(Use 𝜋 = 22/7).

#### Solution

Given that,
Radius of cylinder= 12cm =r_1
Raised in height =6.75cm=h

⇒ Volume of water raised = Volume of the sphere

⇒ πr_1^2h=4/3πr_2^3

⇒ (12xx12xx6.75)=4/3r_2^3

⇒(12xx12xx6.75xx3)/4=r_2^3

⇒r_2^3=729

⇒r_2=9cm

Radius of sphere is 9cm.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 21: Surface Areas and Volume of a Sphere
Ex.21.20 | Q: 27 | Page no. 21
Solution A Cylinder of Radius 12 Cm Contains Water to a Depth of 20 Cm. a Spherical Iron Ball is Dropped into Cylinder and Thus the Level of Water Raised by 6.75 Cm. Find Radius of the Ball. (Use 𝜋 = 22/7). Concept: Volume of a Sphere.
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