Question

Two similar cones have radii in the ratio n:m. What is the ratio of their slant heights?

Answer 1

Answer:

The ratio of the slant heights of the two cones will also be n : m.

Step-by-step explanation:

See the attached diagram.

If we take the vertical sections along any diameter of the base circle of the cones A and B then the triangular sections as we get will be similar.

Now, ratio of the base of the triangles A and B i.e. the ratio of the diameters of the cones A and B will be 2n : 2m = n : m and this will be the same as the ratios of other two sides of the triangles A and B.

Therefore, the ratio of the slant heights of the two cones will also be n : m. (Answer)