Question

Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.

Answer 1

Answer:

The radius of the resulting sphere is 6 cm.

Step-by-step explanation:

SOLUTION :  

Let r1, r2 ,r3 be the radius of the given 3 spheres & R be the radius of a single solid sphere.

Given :  

r1= 3cm, r2 = 4 cm, r3 = 5 cm

Volume of first metallic sphere (V1)= 4/3π(r1)³ = 4/3 π (3)³

Volume of second metallic sphere (V2)= 4/3π(r2)³ = 4/3 π (4)³

Volume of third metallic sphere (V3) = 4/3π(r3)³ = 4/3 π (5)³

Volume of single solid sphere(V) = 4/3πR³

A .T.Q

Volume of 3 metallic spheres = volume of single solid sphere

V1+ V2 + V3 = V

4/3 π (3)³ + 4/3 π (4)³ + 4/3 π (5)³ = 4/3πR³

4/3π(3³ + 4³ + 15³) = 4/3 πR³

27 + 64 + 125 = R³

216 = R³

R = ³√216

R = 6

Hence, the radius of the resulting sphere = 6 cm.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Hope its clear frnd