A metal cuboid with sides in the ratio of 2:4:6 is melted to form small cubes of

Question

A metal cuboid with sides in the ratio of 2:4:6 is melted to form small cubes of side 2 cm. If the sum of all the edges of the cuboid is 144 cm, then find the ratio of the total surface area of the cuboid to the total surface area of the cubes.

Options:

A . 2:1

B . 13:4

C . 11:54

D . 4:1

Answer: Option C
:
C
Sides are in the ratio 2:4:6
Volume of cuboid= 2x .4x . 6x = 48 x

^{3}

Volume of cube= 2.2.2=8
Number of cubes= 6x

^{3}

Length of all edges of the cuboid= 144 =4(2x+4x+6x)

\Rightarrow

x=3cm
Ratio = 2

\frac{[72 + 108 + 216]}{6 (27)}

x 6 x 4
=

\frac{11}{54}

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