Question

a right circular metallic cone of height 20 cm and base radius 5 cm is melted and recast into a solid sphere find the radius of the sphere​

Answer 1

Answer:

r of sphere is 5cm

Step-by-step explanation:

Volume of cone= 1/3πr²h

= 1/3π*5²*20

= 1/3π*500cm³

Volume of cone=Volume of sphere

1/3π*500=4/3πr³

π get cancelled from both the sides

r³ = 3*500/4*3 = 500/4 = 125

r= cube root of 125

Therefore radius of sphere = 5cm

Answer 2

Given:

• Height of the metallic cone = 20cm
• Radius of base = 5cm

To find:

• The radius of the sphere.

Solution:

• As cone is melted and recasted into sphere, the volume of cone and sphere should be same. Therefore,

⇒ Volume of cone = Volume of sphere

⇒ 1/3πr²h = 4/3πR³

⇒ 1/3 × 22/7 × (5)² × 20 = 4/3 × 22/7 × R³

⇒ 5 × 5 × 20 = 4R³

⇒ R³ = (5 × 5 × 20)/4

⇒ R³ = 5 × 5 × 5

⇒ R = 3√(5)³

⇒ R = 5cm

Hence, radius of the sphere is 5cm.

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