area of cone

Question

Students of a class were when asked to make cones from sheets of paper, cones made by I and J had ratio of the curved surface areas equal to 3:4. If the slanting heights of both the cones were equal, and the radius of Jasmine's cone was 8cm. Find the base diameter of the cone made by I.

Answer 1

The curved surface area of a cone is equal to one-half the product of its base perimeter, πR and its slant height, L.

 

The problem states that the slant heights are equal, so Li=Lj.  Consequently, the curved surface areas are proportional to the radii.

 

The ratio of the curved surface areas is 3/4, so

 

Ri/Rj=3/4

 

It is stated that Rj=8.

 

Ri/8=3/4

 

Ri=6

 

Diameter is twice the radius.

 

Di=12