A day full of math games & activities. Find one near you.

A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 1 : 6

Solution:

The cube drawn below represents the cube of side 4 cm cut into 1 cm cubes.

. A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?

Volume of cube with side 4 cm = 4³ = 64 cm³

Volume of cube with side 1 cm = 1³ = 1 cm³

Total number of cubes with side 1 cm = (Volume of cube with side 4 cm) / (Volume of cube with side 1 cm)

= 64 / 1

= 64

The surface area of the 1 cm cubes will be = 6 × side² = 6 × 1² = 6 cm²

Therefore surface area of 64 cubes will be = 64 × 6 = 384 cm²

The surface area of the original cube= 6side² = 6 × (4)² = 96 cm²

The ratio of the surface area of the original cube to the area of 64 cubes with side 1 cm = 96:384 = 1:4

✦Try This: A cube of side 5 cm, is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?

A cube of side 5 cm is cut into 1 cm cubes.

Volume of cube with side 5 cm = 5³ = 125 cm³

Volume of cube with side 1 cm = 1³ = 1 cm³

Total number of cubes with side 1 cm = (Volume of cube with side 5 cm) / (Volume of cube with side 1 cm)

= 125 / 1

= 125

The surface area of the 1 cm cubes will be = 6 × side² = 6 × 1² = 6 cm²

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

The surface area of the original cube = 6side² = 6 × (5)² = 150 cm²

The ratio of the surface area of original cube to the area of 125, 1-cm cubes = 150:750= 1:5

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

NCERT Exemplar Class 8 Maths Chapter 11 Problem 2

Summary:

A 4 cm side cube is cut into 1 cm cubes. The ratio of the surface areas of the original cubes and cut-out cubes is 1:4

☛ Related Questions: