If there spheres of radius 3 cm, 4 cm and 5 cm are melted and cast into a large sphere, then find the radius of the large sphere so formed.

Question

If there spheres of radius 3 cm, 4 cm and 5 cm are melted and cast into a large sphere,
then find the radius of the large sphere so formed.

Answer 1

The total volume of the three spheres is:

 

(4/3)π(3)³ + (4/3)π(4)³ + (4/3)π(5)³

 

= (4/3)π(3³+4³+5³)

 

= (4/3)π(216)

 

= (4/3)π(6)³

 

The "new" sphere would have radius = 6 cm

 

 

Answer 2

Use the formula V=4pi(r³/3) to find the volumes of each sphere given.

 

Here is the 3cm ball done for you...

V=4pi(3³/3)
V=4pi(9/3)
V=4pi(3)
V=12pi
V=37.70

 

 

Add those 3 values together to find out the total volume of material that will go into the new sphere.

 

Use the same formula but solved for (r) to get the new radius.

 

(V/4pi)/3=r³  take the cube root of both sides to find (r) (This program doesn't allow me to easily do write cube roots)