A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone.
Answers
Answer:
The height of the cone is 14 cm.
Step-by-step explanation:
Given :
Internal diameter of hollow sphere = 4 cm
Internal radius of hollow sphere , r = 2 cm
External diameter of hollow sphere = 8 cm
External radius of hollow sphere , R = 4 cm
Diameter of the cone = 8 cm
Radius of the cone , r1 = 4 cm
Volume of the hollow spherical shell = 4/3π(R³ − r³)
Let the height of the cone be h cm.
Volume of the cone = 1/3πr1²h
Since, the hollow spherical shell is melted into a cone , so volume of both are equal
Volume of the hollow spherical shell = Volume of the cone
4/3π(R³ − r³) = 1/3πr1²h
4(R³ − r³) = r1²h
4(4³ - 2³) = 4²h
4(64 - 8) = 16h
4(56) = 16h
h = (4 × 56) /16
h = 56/4 = 14
h = 14 cm
Hence, the height of the cone is 14 cm.
HOPE THIS ANSWER WILL HELP YOU...
Here Given that,
Internal diameter of hollow sphere = 4 cm
Internal radius of hollow sphere = 2 cm
External diameter of hollow sphere = 8 cm
External radius of hollow sphere = 4 cm
Volume of the hollow sphere = 43∏×(43−23)
Then Given,
diameter of the cone = 8 cm
Radius of the cone = 4 cm
Let the height of the cone be x cm
Volume of the cone = 13∏×42×h
Since the volume of the hollow sphere and cone are equal.
So, equating equations i and ii, we get the,
43∏×(42−22)= 13∏×42×h
H= 12 cm
The height of the cone so formed is having a height of 12 cm.
Hope its help you