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A Cone of Height 20 Cm and Radius of Base 5 Cm is Made up of Modelling Clay. a Child Reshapes It in the Form of a Sphere. Find the Diameter of - Mathematics

Sum

A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere. 

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Solution

We have,

the base radius of the cone, r=5 cm and 

the height of the cone, h = 20 cm

Let the radius of the sphere be R.

As,

Volume of sphere = Volume of cone 

`rArr 4/3piR^3 = 1/3pir^2h`

`rArr R^3 = (pir^2hxx3)/(3xx4pi)`

`rArr R^3 = (r^2h)/4`

`rArr R^3 = (5xx5xx20)/4`

`rArr R^3 = 125`

`rArr R = root(3)(125)`

⇒ Diameter of the sphere = 2R= 2×5 = 10 cm


So, the diameter of the sphere is 10 cm.

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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise 19B | Q 2 | Page 897
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