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A parallelopiped whose sides are in ratio 2 : 4 : 8 have the same volume as a cube. The ratio of their surface area is :
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- 7 : 5
- 4 : 3
- 8 : 5
- 7 : 6
- 7 : 5
Correct Option: D
Let the sides of the parallelopiped be 2x, 4x and 8x units respectively and the edge of cube be y units.
∴ 2x × 4x × 8x = y³
⇒ 8 × 8 x3 = y³
Taking cube roots,
⇒ 4x = y .....(i)
Surface area of parallelopiped = 2 (2x × 4x +4x ×8x + 8x × 2x)
= 2 (8x² + 32x² + 16x²) = 112x² sq. units.
Surface area of cube = 6y² sq. units.
∴ Required ratio = | = | |||
6y² | 6 × 16x² |
= | or 7 : 6 | |
6 |