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A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is __________

Solution:

A cube of 5 cm edge will have a volume = 5 × 5 × 5 = 125 cm³

If this cube is cut into cubes with1 cm edges then the number of cubes will be 125

The volume each 1 cm edge cube will be 1cm³ (1cm × 1 cm × 1cm)

Hence the volume of 125 cubes will be = 125 × 1 = 125 cm³

The percentage increase in volume will be therefore 0% or none. In other words there will be no increase in volume.

✦ Try This: A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in surface area after such cutting is __________.

A cube of 5 cm edge (s = 5) will have a volume = 6s² = 6 × 5 × 5 = 150 cm²

If this cube is cut into cubes with1 cm edges then the number of cubes will be 125

The surface area each 1 cm edge (s = 1) cube will be 6 × 1cm² (6s²) = 6cm²

Hence the surface area of 125 cubes will be = 125 × 6 = cm²

The percentage increase in volume will be therefore

Increase in Volume = (750 - 150)/150 × 100 = ( 600/150) × 100 = 400%

A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in surface area after such cutting is 400%.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 30

Summary:

A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is none

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