V<sub>1</sub>, V<sub>2</sub>, V<sub>3</sub> and V<sub>4</sub> 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 :<br>(i) V<sub>1</sub> + V<sub>2</sub> + 2V<sub>3</sub> 4<br>(ii) V<sub>1</sub> + 4V<sub>2</sub> + V<sub>3</sub> 4<br>(iii) 2(V<sub>1</sub> + V<sub>3</sub>) + V<sub>2</sub> = V<sub>4</sub><br>Which of these statements area correct ?
Correct Answer: 1, 2 and 3
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 4
(ii) V1 + 4V2 + V3
= x3 + 4 × 8x3 + 27 x3
= 60x3 4
(iii) 2(V1 + V3) + V2
= 2 (x3 + 27x3) + 8x3
= 64x3 = V4
V1 = x3,
V2 = (2x)3 = 8x3
V3 = (3x)3 = 27x3
V4 = (4x)3 = 64x3
(i) V1 + V2 + 2V3
= x3 + 8x3 + 2 × 27x3
= 63x3 4
(ii) V1 + 4V2 + V3
= x3 + 4 × 8x3 + 27 x3
= 60x3 4
(iii) 2(V1 + V3) + V2
= 2 (x3 + 27x3) + 8x3
= 64x3 = V4
