Math, asked by Vishnu73, 1 year ago

A hollow sphere of internal and external diameter 4cm and 8cm respectively is melted to form a cone of base with diameter 8cm. Find the height of the cone.

Answers

Answered by nikitasingh79
352
•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.

HOPE THIS WILL HELP YOU..
Answered by princess489
202
here is your answer.... may it will. help you...
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