During conversion of a solid from one shape to another, the volume of ...
Introduction:
When a solid undergoes a shape transformation, such as stretching, bending, or compressing, the volume of the new shape can change. This change in volume depends on the nature of the transformation and the properties of the material.
Explanation:
The volume of a solid is a measure of the amount of space it occupies. It is calculated by multiplying the area of the base of the solid by its height. When a solid undergoes a shape transformation, the base and height of the solid may change, resulting in a change in volume.
Example:
Let's consider the example of a cylindrical solid being transformed into a cone. The cylindrical solid has a circular base and a constant height. As the shape transforms into a cone, the base of the solid changes from a circle to a smaller circle, while the height remains the same.
Effect on volume:
When the base of the solid changes, the area of the base also changes. Since the volume of a solid is directly proportional to the base area, any change in the base area will result in a change in volume.
In this specific example, as the cylindrical solid transforms into a cone, the base area decreases since the radius of the base decreases. However, the height remains the same. As a result, the volume of the cone will be less than the volume of the cylindrical solid.
Conclusion:
In general, during the conversion of a solid from one shape to another, the volume of the new shape can either increase or decrease depending on the specific transformation. However, in some cases, such as when the height remains constant and only the base area changes, the volume of the new shape will remain unaltered. Therefore, the correct answer is option 'C' - the volume will remain unaltered.
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