Question

A hollow sphere of external and internal diameter 6cm and 4cm respectively is melted into a cone of base diameter 8cm.Find the height of the cone.

Answer 1

Answer:

Step-by-step explanation:

•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) = 6 cm.

external radius of hollow sphere( R )= 6/2= 3 cm.

Volume of the Hollow sphere = 4/3π(R³ - r³)

Volume of the Hollow sphere = 4/3π(3³ - 2³)

Volume of the Hollow sphere = 4/3π(27 - 8)

Volume of the Hollow sphere = 4/3π(19) 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(19)

16h = 4 ×19

h = (4 × 19)/16

h = 19/4 = 4.75cm

Hence, the height of the cone is 14 cm.

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Answer 2

Step-by-step explanation:

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