Question

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.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

Given:


Height of cone (h)= 20 cm


Radius of cone radius of cone (r1)= 5 cm


Volume of cone= (⅓)πr1²h


Volume of cone= (⅓)× π × 5²×20


= (25×20)π/ 3 = 500π/3


Volume of cone=500π/3 cm³



Let radius of sphere= r2


Volume of sphere=( 4/3)πr2³


=( 4/3)×π×(r2)³= 4πr2³/3


Volume of sphere= 4πr2³/3


Child reshapes cone with Sphere

So , volume of Sphere= volume of cone


4πr2³/3 = 500π/3


4r2³= 500


r2³= 500/4= 125


r2³= 125


r2=³√125


r2= 5 cm


Diameter of the sphere = 2× radius= 2× 5 = 10 cm

Hence, the Diameter of the sphere= 10 cm


HOPE THIS WILL HELP YOU...

Answer 2

heya

it's too easy.

volume of cone =1/3πr^2h

=)1/3×22/7*5*5*20

=)500π/3

and now

according to ur question a child reshape it in sphere .

but it's volume remain same as cone

so,

so,volume of a sphere is =4/3πr^3=500π/3

r^3=500/4

r^3=125

r=3√125

r=5.cm

so,diameter =2radius .

diameter=2*5

=10cm

hope it help you.

.@rajukumar☺