Remoulding (Leaving Cert Mathematics): Revision Notes

Remoulding

What is Remoulding?

Remoulding refers to the process of reshaping or reforming a solid object into a new shape without altering its material. This concept is commonly used in geometry problems where a solid is melted or reshaped, and the total volume remains constant.

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Key Principles of Remoulding

Volume Conservation:

The volume of the original object equals the volume of the remoulded object.

$$V_{\text{original}} = V_{\text{remoulded}}$$

Shapes May Change, but the Material Stays the Same:

The remoulded object may have a different surface area or dimensions, but the volume remains constant.

Common Scenarios:

• Melting a solid to form another shape (e.g., melting a sphere into a cylinder).
• Cutting a shape and rearranging it into another form.

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Worked Examples

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Summary

• Remoulding Principle: The volume of the original and remoulded shapes is always equal.
• Volume Conservation Formula: $V_{\text{original}} = V_{\text{remoulded}}$
• Common applications involve transitioning between spheres, cylinders, cubes, and other shapes.
• Use the specific volume formula for each shape to solve remoulding problems.
• Practice with various geometrical shapes to enhance problem-solving skills.