A solid right circular cone of diameter 14cm and height 8cm is melted to form a hollow sphere. If the external diameter of the sphere is 10cm, find the internal diameter of the sphere.
Answers
Step-by-step explanation:
Diameter of cone=14 cm
so, Radius of cone= 7cm
Height of cone= 8cm
∴ Volume of cone= 1/3*pi*r^2*h
=1/3*pi*49*8 cm^3
In Sphere, External Radius R=5cm
Let, Internal Radius = r
Volume of Sphere = External Volume- Internal Volume
= 4/3*pi*R^3-4/3*pi*r^3
=4/3*pi[R^3-r^3]
=4/3*pi[5^3-r^3]
But During Conversion Volume Remains Same
So, Volume of Sphere=Volume of Cone
4/3*pi[125-r^3]= 1/3*pi*49*8
4[125-r^3]=49*8
[125-r^3]=49*2
r^3=125-98
r^3=27
so, r =3 cm
Internal Radius= 3cm
So, Internal Diameter=3*2= 6cm
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