Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio $$4:3$$.
Correct option is A. $$4:3$$.
We have,
diameters are equal, i.e. $$r_1=r_2$$ and slant heights are in the ratio $$4:3$$, i.e. $$l_1=4x, l_2=3x$$.
We know, curved surface area of a cone, $$S=\pi r l$$.
$$\therefore $$ Ratio ofthe curved surface areas of the cones
$$=\dfrac{S_1}{S_2}=\dfrac{\pi r_1l_1}{\pi r_2l_2}=\dfrac{l_1}{l_2}=\dfrac{4}{3}$$.
Hence, the required ratio is $$4:3$$.