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A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes?

Solution:

A cube of side 5 cm if cut into cubes of 1cm side then the number of cubes formed will be 125 in number.

The surface area of the 5cm cube = 6s² = 6(5)² = 6 × 25 = 150 cm²

The surface area of each 1 cm cube = 6s² = 6(1)² = 6 × 1 = 6cm²

The surface area of the 125 cubes will be = 6 × 125 = 750cm²

The ratio of the surface area of the original cube to the sum of the surface areas of the smaller cubes = 150/750 = ⅕ or 1:5

✦ Try This: A cube of side 4 cm is cut into as many 1 cm cubes as possible. The ratio of the surface area of the original cube to that of the sum of the surface areas of

the smaller cubes?

A cube of side 4 cm if cut into cubes of 1cm side then the number of cubes formed will be 64 in number.

The surface area of the 4cm cube = 6s² = 6(4)² = 6 × 16 = 96 cm²

The surface area of each 1 cm cube = 6s² = 6(1)² = 6 × 1 = 6cm²

The surface area of the 125 cubes will be = 6 × 64 = 384cm²

The ratio of the surface area of the original cube to the sum of the surface areas of the smaller cubes = 96/384 = 1/4 or 1:4

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

NCERT Exemplar Class 8 Maths Chapter 11 Problem 87

A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes?

Summary:

A cube of side 5 cm is cut into as many 1 cm cubes as possible. The ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes will be 1:5

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