A) 2 : 3
B) 4 : 5
C) 5 : 4
D) 3 : 2
Correct Answer: C
Solution :
Diameter of first cone = Diameter of second cone \[\frac{\text{Slant}\,\text{height}\,\text{of}\,\text{first}\,\text{cone}({{l}_{1}})}{\text{Slant}\,\text{height}\,\text{of}\,\text{second}\,\text{cone}({{l}_{2}})}\] \[\Rightarrow \]\[\frac{\text{Curved}\,\text{surface}\,\text{area}\,\text{of}\,\text{first}\,\text{cone}}{\text{Curved}\,\text{surface}\,\text{area}\,\text{of}\,\text{the}\,\text{second}\,\text{cone}}\] \[\text{=}\frac{\pi {{r}_{1}}{{l}_{1}}}{\pi {{r}_{2}}{{l}_{2}}}=\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)\left( \frac{{{l}_{1}}}{{{l}_{2}}} \right)=1\times \frac{5}{4}=\frac{5}{4}\] Hence, the ratio of their curved surface areas is 5:4.
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