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Proportionality of Volume Video Lecture | Quantitative Aptitude (Quant) - CAT

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FAQs on Proportionality of Volume Video Lecture - Quantitative Aptitude (Quant) - CAT

1. What is the principle of proportionality in relation to volume?
Ans. The principle of proportionality in relation to volume refers to the idea that the volume of an object is directly related to its dimensions. For example, if an object’s dimensions are scaled by a certain factor, its volume will change by the cube of that factor. This principle is fundamental in geometry and physics when analyzing the properties of three-dimensional shapes.
2. How does proportionality of volume apply to similar geometric shapes?
Ans. In similar geometric shapes, the proportionality of volume indicates that if two shapes are similar and their corresponding linear dimensions are in the ratio of \( k \), then their volumes will be in the ratio of \( k^3 \). This means if one shape is twice the size of another, its volume will be \( 2^3 = 8 \) times greater than that of the smaller shape.
3. Can you provide an example of proportionality of volume in real life?
Ans. A practical example of proportionality of volume can be seen in cooking. When you double the size of a recipe, you must increase both the ingredients and the cooking vessel size. If the original pot holds 1 liter, to accommodate double the recipe, you would need a pot with a volume of 8 liters, since \( (2)^3 = 8 \), highlighting the cubic relationship.
4. How can understanding volume proportionality be useful in engineering?
Ans. Understanding volume proportionality is crucial in engineering for designing structures and components. For instance, when scaling up a model of a bridge for testing, engineers must calculate the new volume to ensure the materials used can support the increased load without compromising safety. This ensures that the scaled model accurately reflects the properties of the full-sized structure.
5. What are the mathematical formulas related to volume proportionality?
Ans. The key mathematical formula related to volume proportionality is \( V = k^3 \cdot V_0 \), where \( V_0 \) is the original volume, \( k \) is the scale factor for the linear dimensions, and \( V \) is the new volume after scaling. This formula helps in determining the volume of shapes when they are scaled up or down.
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