Two cubes have volumes in the ratio 1:64. The ratio of the area of a face of first cube to that of the other is
(a) 1:4
(b) 1:8
(c) 1:16
(d) 1:32

Solution:

Let V₁ = Volume of Cube 1 = S₁³

Let V₂ = Volume of Cube 2 = S₂³

V₁/V₂ = 1/64

S₁³/S₂³ = 1/64

S₁/S₂ = ¼ (1)

The ratio of the area of a face of first cube to that of the other will be given by the square of equation (1) as area of any face of a cube with side S is S².

S₁²/S₂² = (¼)²

S₁²/S₂² = 1/16

The correct choice for the answer is (c ).

✦ Try This: Two cubes have volumes in the ratio 1:27. The ratio of the area of a face of first cube to that of the other is (a) 1:3, (b) 1:9, (c) 1:18, (d) 1:27

Let V₁ = Volume of Cube 1 = S₁³

Let V₂ = Volume of Cube 2 = S₂³

V₁/V₂ = 1/27

S₁³/S₂³ = 1/27

S₁/S₂ = 1/3 (1)

The ratio of the area of a face of first cube to that of the other will be given by the square of equation (1) as area of any face of a cube with side S is S².

S₁²/S₂² = (1/3)²

S₁²/S₂² = 1/9

The correct choice for the answer is (b).

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

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NCERT Exemplar Class 8 Maths Chapter 11 Problem 25

Two cubes have volumes in the ratio 1:64. The ratio of the area of a face of first cube to that of the other is (a) 1:4 (b) 1:8 c) 1:16 (d) 1:32

Summary:

Two cubes have volumes in the ratio 1:64. The ratio of the area of a face of first cube to that of the other is 1:16

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