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A Cylindrical Tube of Radius 12cm Contains Water to a Depth of 20cm. a Spherical Ball of Radius 9cm is Dropped into the Tube and Thus Level of Water is Raised by Hcm. What is the Value of H_____? - CBSE Class 10 - Mathematics

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Question

A cylindrical tube of radius 12cm contains water to a depth of 20cm. A spherical ball of radius 9cm is dropped into the tube and thus level of water is raised by hcm. What is the value of h.

Solution

Given that radius of cylindrical tube (r1) = 12cm

Let height of cylindrical tube (h)

Volume of a cylinder = `pir_1^2h`

v1 = π(12)2 x h                 ............(1)

Given spherical ball radius (r2) = 9cm

Volume of sphere = `4/3pir_2^3`

`v_2=4/3xxpixx9^2`      ..............(2)

Equating (1) and (2)

v1 = v2

`pi(12)^2xxh=4/3xxpixx9^3`

`h=(4/3xxpixx9^3)/(pi(12)^2)`

h = 6.75cm

Level of water raised in tube (h) = 6.75cm

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APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Ex. 14.10 | Q: 43 | Page no. 30
Solution A Cylindrical Tube of Radius 12cm Contains Water to a Depth of 20cm. a Spherical Ball of Radius 9cm is Dropped into the Tube and Thus Level of Water is Raised by Hcm. What is the Value of H_____? Concept: Volume of a Combination of Solids.
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