A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm.
Answers
Answer:
2 x 4 x 4
32
32 x 3
96
Step-by-step explanation:
Answer:
The height of the cone is 14 cm & Slant height of the cone is 14.56 cm.
Step-by-step explanation:
Given :
Let the height of the cone be h cm.
Internal radius of hollow sphere ,r = 2 cm
External radius of hollow sphere , R = 4 cm
Radius of the cone , r1 = 4 cm
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
Height of the cone = 14 cm.
Slant height of the cone, l = √ r² + h²
l = √4² + 14²
l = √16 + 196
l = √212
l = 14.56 cm
Slant height of the cone = 14.56 cm.
Hence, the height of the cone is 14 cm & Slant height of the cone is 14.56 cm.
Hence, HOPE THIS ANSWER WILL HELP YOU...