The diameter of two cones are equal if their slant height are in the ratio 5:4, find the ratio of their curved surface area
surface area of similar objects varies directly with the square of their corresponding sides
ratio of surface areas
= 5^2 : 4^2
= 25 : 16
Hmmm. I interpret the problem to be that the cones have the same diameter. Hence, the same base radius.
Since the curved surface area is πrs, if r is constant, then the area is proportional to s, so it is also in the ratio 5:4.
To find the ratio of the curved surface area of two cones, we first need to find the formulas for the curved surface area of a cone.
The formula for the curved surface area (CSA) of a cone is given by
CSA = π * r * l
where r is the radius of the base and l is the slant height.
Since we are given that the diameter of the two cones is equal, we know that the radius will be equal as well.
Let's assume the radius of the first cone is r1 and the slant height is l1. Similarly, let's assume the radius of the second cone is r2 and the slant height is l2.
According to the given information, we have the following ratios:
l1 : l2 = 5 : 4
Since the diameter of the two cones is equal, we know the radii will be equal as well:
r1 = r2
Now, we can set up the ratios for the curved surface areas:
CSA1 : CSA2 = π * r1 * l1 : π * r2 * l2
Since r1 = r2, we can cancel them out:
CSA1 : CSA2 = l1 : l2
Substituting the given ratio of l1 : l2 = 5 : 4, we get:
CSA1 : CSA2 = 5 : 4
Therefore, the ratio of the curved surface areas of the two cones is 5 : 4.