A parallelopiped whose sides are in ration 2 : 4 : 8 has the same volume as a cube. The ratio of their surface areas is:

Let length of parallelopiped = $$2x$$ units

Breadth = $$4x$$ units and height = $$8x$$ units

Let side of cube = $$a$$ units

Acc. to ques, volume of cube = volume of parallelopiped

=> $$a^3 = 2x \times 4x \times 8x$$

=> $$a^3 = 64 x^3$$

=> $$a = \sqrt[3]{64x} = 4x$$ units

Now, surface area of parallelopiped = $$2 (lb + bh + hl)$$

= $$2 (8x^2 + 32x^2 + 16x^2)$$

= $$2 \times 56 x^2 = 112x^2$$ sq. units

Surface area of cube = $$6 a^2$$

= $$6 (4x)^2 = 96x^2$$

$$\therefore$$ Required ratio = $$\frac{112 x^2}{96 x^2}$$

= $$7 : 6$$