a) 2 : 1
b) 3 : 2
c) 25 : 18
d) 27 : 20
Answer: c
Explanation:
$$\eqalign{
& {\text{Volume}}\,{\text{of}}\,{\text{the}}\,{\text{large}}\,{\text{cube}} \cr
& = \left( {{3^3} + {4^3} + {5^3}} \right) = 216\,c{m^3} \cr
& {\text{Let}}\,{\text{the}}\,{\text{edge}}\,{\text{of}}\,{\text{the}}\,{\text{large}}\,{\text{cube}}\,{\text{be}}\,a \cr
& So,\,{a^3} = 216\,\,\,\,\, \Rightarrow \,\,\,\,\,a = 6\,cm \cr
& {\text{Required}}\,{\text{ratio}} = {\frac{{6 \times \left( {{3^2} + {4^2} + {5^2}} \right)}}{{6 \times {6^2}}}} \cr
& = \frac{{50}}{{36}} \cr
& = 25:18 \cr} $$
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