Question

A metallic
sphere diameter 8.4 cm is melted
and recast into the shape of a cylinder of
diameter 12 cm Find the night of the cylindey.​

Answer 1

Correct Question

A metallic sphere diameter 8.4 cm is melted and recast into the shape of a cylinder of diameter 12 cm Find the height of the cylinder.

Answer

• Height of the cylinder is 2.744 cm

Explanation

Given

• There is a sphere of diameter 8.4 cm
• It is melted to make a cylinder of diameter 4 cm

To Find

• Height of the cylinder

Solution

We know that both the cylinder and the sphere will have the same volume which means if we equate these two volumes then we will be able to find the height!!

✭ Radius of the two Figures

→ Radius (Sphere) = Diameter/2

→ Radius (Sphere) = 8.4/2

→ Radius (Sphere) = 4.2 cm

Similarly,

→ Radius (Cylinder) = Diameter/2

→ Radius (Cylinder) = 12/2

→ Radius (Cylinder) = 6 cm

✭ Volume of the sphere

→ Volume (Sphere) = 4/3 πr³

→ Volume (Sphere) = 4/3 × π × 4.2³

→ Volume (Sphere) = 4/3 × π × 74.088

→ Volume (Sphere) = 98.784π cm³

✭ Volume of Cylinder

→ Volume (Cylinder) = πr²h

→ Volume (Cylinder) = π × 6² × h

→ Volume (Cylinder) = π × 36 × h

→ Volume (Cylinder) = 36πh

✭ Height of the Cylinder

→ Volume of Cylinder = Volume of Sphere

→ 98.784π = 36πh

→ 98.784/36 = h

→ Height = 2.744 cm

Answer 2

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A metallic sphere diameter 8.4 cm is melted and recast into the shape of a cylinder of diameter 12 cm Find the night of the cylinder.

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