Question
V1, V2, V3 and V4 are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4 cm respectively. Some statements regarding these volumes are given below :
(i) V1 + V2 + 2V3 < V4
(ii) V1 + 4V2 + V3 < V4
(iii) 2(V1 + V3) + V2 = V4
Which of these statements area correct ?
(i) V1 + V2 + 2V3 < V4
(ii) V1 + 4V2 + V3 < V4
(iii) 2(V1 + V3) + V2 = V4
Which of these statements area correct ?
Answer: Option D
Clearly, we have :
V1 = x3,
V2 = (2x)3 = 8x3
V3 = (3x)3 = 27x3
V4 = (4x)3 = 64x3
(i) V1 + V2 + 2V3
= x3 + 8x3 + 2 × 27x3
= 63x3 < V4
(ii) V1 + 4V2 + V3
= x3 + 4 × 8x3 + 27 x3
= 60x3 < V4
(iii) 2(V1 + V3) + V2
= 2 (x3 + 27x3) + 8x3
= 64x3 = V4
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Clearly, we have :
V1 = x3,
V2 = (2x)3 = 8x3
V3 = (3x)3 = 27x3
V4 = (4x)3 = 64x3
(i) V1 + V2 + 2V3
= x3 + 8x3 + 2 × 27x3
= 63x3 < V4
(ii) V1 + 4V2 + V3
= x3 + 4 × 8x3 + 27 x3
= 60x3 < V4
(iii) 2(V1 + V3) + V2
= 2 (x3 + 27x3) + 8x3
= 64x3 = V4
Was this answer helpful ?
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