Question

a solid right circular cylinder is made of clay whose diameter is 4cm and height is 48cm. Reema wants to make a number of spheres with diameter 4cm. how many spheres can be made out of it?​

Answer 1

ANSWER :-

• 18 spheres can be made.

GIVEN :-

• Diameter of cylinder = 4cm
• Height of cylinder = 48cm
• Diameter of each sphere = 4cm

TO FIND :-

• Number of spheres made.

TO KNOW :-

★ Volume of Cylinder = πr²h

★ Volume of Sphere = (4/3)πr³

★ Radius = (1/2) × Diameter

SOLUTION :-

We know ,

★ Radius = 1/2 of Diameter

So,

• Radius of Cylinder(R) = (1/2)4 = 2cm
• Radius of Sphere(r) = (1/2)4 = 2cm
• Height of Cylinder = 48cm

As we know that cylinder to converted to small spheres. So, volume will remain same .

Volume of Cylinder = Volume of Total spheres

Let the total spheres formed be 'n'.

Volume of Cylinder = n × Volume of one sphere

→ πR²h = n × (4/3)πr³

Cancelling 'π' from both sides ,

→ R²h = n × (4/3)r³

Putting values we get...

→ 2² × 48 = n × (4/3) × 2³

→ 4 × 48 = n × (4/3) × 8

→ 192 = n × (32/3)

→ n = 192 × (3/32)

→ n = 576/32

→ n = 18

Hence , 18 small spheres are formed.

MORE TO KNOW :-

★ Volume of cube = edge³

★ Volume of cuboid = l × b × h

★ Volume of hemisphere = (2/3)πr³

★ Volume of cone = (1/3)πr²h