Question

Aa right circular cone is 8cm height and the radius of base is 2cm. The come is melted and recast into a sphere determine the diameter of sphere

Answer 1

Given :-

• A right circular cone is 8cm height and the radius of base is 2cm. The cone is melted and recast into a sphere

To find :-

• Diameter of sphere

Solution :-

• Height of cone = 8cm

• Radius of cone = 2cm

It is given that cone is melted and recast into a sphere.

So,

→ Volume of cone = volume of sphere

→ ⅓ πr²h = 4/3 πr³

Where " r " is radius and " h " is height

According to question

→ ⅓ πr²h = 4/3 πr³

→ Cancel π and ⅓

→ r²h = 4r³

Put the values

→ (2)² × 8 = 4r³

→ 4 × 8 = 4r³

→ 32 = 4r³

→ r³ = 32/4

→ r³ = 8

→ r = ³√8

→ r = 2cm

Hence,

• Radius of sphere = 2cm

• Diameter of sphere = 2 × radius = 4cm

Answer 2

Answer:

d= 4cm

Step-by-step explanation:

Volume of cone = 1/3πr²h

= 1/3 X 3.14 X 2² X 8

= 33.49

Volume of sphere = 4/3πr³

33.49 = 4/3 X 3.14 X r³

r³ = (33.49 X 3) / (4 X 3.14)

r³ = 8

r = 2

D = 2X2

= 4