Question

hollow sphere of external and internal diameter 8 cm and 4 cm respectively is melted into a solid cone of base diameter 8 cm find the height of the cone

Answer 1

•If solid of one shape is converted into solid of another shape, then Total volume of the solid to be converted =  Total volume of the solid into which the given solid is to be converted.

SOLUTION :
Given : Internal diameter of hollow sphere(d)= 4 cm.
Internal radius of hollow sphere (r) = 4/2= 2 cm
external diameter of hollow sphere (D) = 8 cm.
external radius of hollow sphere( R )= 8/2= 4 cm.

Volume of the Hollow sphere = 4/3π(R³ - r³)
Volume of the Hollow sphere = 4/3π(4³ - 2³)
Volume of the Hollow sphere = 4/3π(64 - 8)
Volume of the Hollow sphere = 4/3π(56) cm³

Diameter of the cone(d1) = 8 cm
radius of the cone( r1)= 8/2 = 4 cm

Let the height of the cone be h cm.
Volume of the cone = ⅓ πr1²h
= ⅓ π × 4² × h = 16πh/3

Volume of the cone = Volume of the hollow sphere
16πh/3 = 4/3π(56)
16h = 4 ×56
h = (4 × 56)/16
h = 56/4 = 14 cm

Hence, the height of the cone is 14 cm.

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Answer 2

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.

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