A metallic sphere of radius 4.2 cm is melted and recast into which shape of first cylinder of radius 6 cm. find the height of the Cylinder?

Question

Answer

Answer

Answer

Volume of the Sphere
To find the height of the cylinder created from the melted metallic sphere, we first need to calculate the volume of the sphere.
- The formula for the volume of a sphere is given by:
Volume (V) = (4/3) * π * r³
where r is the radius of the sphere.
- For a sphere with a radius of 4.2 cm:
V = (4/3) * π * (4.2)³
V ≈ (4/3) * π * 74.088
V ≈ 310.4 cm³ (approximately, using π ≈ 3.14)
Volume of the Cylinder
Next, we use the volume of the cylinder to find its height.
- The formula for the volume of a cylinder is:
Volume (V) = π * r² * h
where r is the radius and h is the height.
- Given the cylinder's radius of 6 cm, we can set up the equation:
310.4 = π * (6)² * h
310.4 = π * 36 * h
Solving for Height (h)
Now, we need to isolate h:
- Rearranging the equation gives:
h = 310.4 / (π * 36)
h ≈ 310.4 / (3.14 * 36)
h ≈ 310.4 / 113.04
h ≈ 2.744 cm (approximately)
Conclusion
The height of the cylinder formed from the melted metallic sphere is approximately 2.74 cm.

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