Question

A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?

• A. 10
• B. 1000
• C. 100
• D. 1

Answer 1

Answer:

B. 1000

Understanding Volume and Unit Conversion for Solid Geometry Problems

• Key Concept: Volume of a Cube
  The volume of a cube is calculated by cubing the length of its side (V = side³).

• Importance of Unit Consistency
  When dealing with measurements in different units (meters and centimeters in this case), it is crucial to convert them to a single, consistent unit before performing calculations. This prevents errors and ensures accurate results.

• Unit Conversion: Meters to Centimeters
  * 1 meter (m) is equal to 100 centimeters (cm).
  * This conversion is fundamental in many geometry and physics problems encountered in competitive exams.

• Calculating the Volume of the Large Cube
  * Side of the large cube = 1 meter = 100 cm.
  * Volume of the large cube = (100 cm)³ = 1,000,000 cubic centimeters (cm³).

• Calculating the Volume of a Small Cube
  * Side of each small cube = 10 cm.
  * Volume of one small cube = (10 cm)³ = 1,000 cubic centimeters (cm³).

• Determining the Number of Small Cubes
  To find how many small cubes can be obtained from the large cube, divide the volume of the large cube by the volume of one small cube.
  * Number of small cubes = (Volume of large cube) / (Volume of one small cube)
  * Number of small cubes = 1,000,000 cm³ / 1,000 cm³ = 1000.

• Shortcut/Formulaic Approach
  For problems where a larger cube is cut into smaller identical cubes, the number of smaller cubes can be directly calculated as: (Side of large cube / Side of small cube)³.
  * In this case: (100 cm / 10 cm)³ = (10)³ = 1000