Question

2. If threespheres ofradii3cm,4cm, and 5cmare melted to formasold sphere, then find its radius.​

Answer 1

ANSWER

6cm is the radius of the new sphere formed.

EXPLANATION:

Three spheres are melted to form a new sphere, So, the volume of the three spheres and the volume of the new sphere must be equal.

FORMULA USED:

Volume of a sphere = (4/3)π × (radius)³

SOLUTION

• Volume of the sphere with radius 3cm = (4/3)π(3cm)³

• Volume of the sphere with radius 4cm = (4/3)π(4cm)³

• Volume of the sphere with radius 5cm = (4/3)π(5cm)³

Let the radius of the new sphere formed = a

volume of the new sphere = (4/3)π(a)³

The equation becomes:

⟹ (4/3)π(a)³ = (4/3)π(3cm)³ + (4/3)π(4cm)³ + (4/3)π(5cm)³

Taking (4/3)π in common:

⟹ (4/3)π(a)³ = (4/3)π[ (3cm)³ + (4cm)³ + (5cm)³ ]

Dividing both sides by (4/3)π

⟹ a³ = (3cm)³ + (4cm)³ + (5cm)³

⟹ a³ = 27cm³ + 64cm³ + 125cm³

⟹ a³ = 216cm³

⟹ a = ³√(216cm³)

⟹ a = 6cm

Radius of the new sphere = a = 6cm