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  1. A parallelopiped whose sides are in ratio 2 : 4 : 8 have the same volume as a cube. The ratio of their surface area is :
    1. 7 : 5
    2. 4 : 3
    3. 8 : 5
    4. 7 : 6
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 =
112x²
=
112x²
6y²6 × 16x²

=
7
or 7 : 6
6



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