The internal and external diameters of a hollow metallic hemispherical shell are 6 cm and 10 cm respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.
Answers
Answer:
Step-by-step explanation:
To answer this question we need to get the volume of the hollow hemispherical metallic shell.
Since it is hollow we need to get the volume of the metallic part.
We need to get the formula of the volume of the hemisphere.
Volume = 2/3πr^3
The volume of the metallic part is :
= Volume of the outer Hemisphere - Volume of inner hemisphere
Volume of outer hemisphere is:
Diameter = 10
Radius = 10/2 = 5
= 2/3 × 3.142 × 5^3 = 261.83 cubic centimeters.
Volume of inner hemisphere :
Diameter = 6
Radius = 6/2 = 3
= 2/3 × 3.142 × 3^3 = 56.556 cubic centimeters.
The volume of the metallic part is :
261.83 - 56.556 = 205.274 cubic centimeters.
This is the volume of the metallic part and it is also the volume of the cone formed.
Volume of a cone = 1/3πr^2h
205.274 = 1/3 × 3.142 × (14/2)^2 × h
205.274 = 51.319h
h = 205.274/51.319
h = 3.99996
This is approximately 4 cm.
The height of the cone is thus :
= 4 cm
The height of cone so formed is 4 cm.
