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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsMensuration : Length, Area, and VolumeIntroduction to Measurements

### Introduction to Measuring Volume

This topic introduced measuring volume as "space-span". It is a derived standard and measured in reference to a standard 1xx1xx1 cube.

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Length of a rod is the distance-span measured in meter.

Area of a surface is the surface-span measured in square meter.

For a solid object that occupies space (like an apple, or a box), what is the measure of the space?

• area is the only possible measure
• volume is the the space-span of a solid
• volume is the the space-span of a solid

The answer is "volume is the the space-span of a solid".

To specify distance-span or length, a reference-prototype-standard (ie a metal rod of specific material at specific temperature) is used.

To specify surface-span or area, the area of a square with 1 meter sides is used as the reference.

Which of the following helps to specify space-span?

• a new reference-prototype-standard for space
• measurement of space-span can be derived from the already defined measure for length
• measurement of space-span can be derived from the already defined measure for length

The answer is "measurement of space-span can be derived from the already defined measure for length".

To specify the space-span or volume of a solid, a cube of side 1 meter is taken as the reference. The volume of that is one cubic meter or 1m^3. In the figure, the reference is shown at the top-right corner. Volume of a solid is given in reference to the volume of a cube of side 1 meter. In the figure, the volume of the given cuboid is the number of 1 cubic meter cubes fit in that cuboid. It is counted to 6, so the volume of the cuboid is 6m^3.

Volume of a solid : The space-span of a solid is the volume of the solid. It is measured in cubic meter (or in one of other derived or similar forms.) Volume is specified as a number in reference to the space-span of a cube of 1 meter side.

Which of the following explains the statement "volume of a box is 3 cubic meter"?

• it is just volume
• The space-span of the box equals 3 space-spans of a cube of side 1 meter
• The space-span of the box equals 3 space-spans of a cube of side 1 meter

The answer is "The space-span of the box equals 3 space-spans of a cube of side 1 meter".

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