a) 1 : 3
b) 2 : 3
c) 5 : 9
d) 7 : 9
Answer: d
Explanation: Let the length of each edge of each cube be a
Then, the cuboid formed by placing 3 cubes adjacently has the dimensions 3a , a and a
Surface area of the cuboid :
$$\eqalign{
& = 2\left[ {3a \times a + a \times a + 3a \times a} \right] \cr
& = 2\left[ {3{a^2} + {a^2} + 3{a^2}} \right] \cr
& = 14{a^2} \cr} $$
Sum of surface area of 3 cubes :
$$\eqalign{
& = \left( {3 \times 6{a^2}} \right) \cr
& = 18{a^2} \cr} $$
Required ratio :
$$\eqalign{
& = 14{a^2}:18{a^2} \cr
& = 7:9 \cr} $$
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