Question 1136820: 2 solid cones are geometrically similar and the height of one cone is 1.5 times that of the other. Given that the height of the smaller cone is 12 cm and its surface area is 124cm², find
i) height
ii) surface area, of the larger cone.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The 1.5 factor is the scale factor between the two similar cones; it is the 3:2 ratio between any linear measurements of the two cones.
If the height of the smaller cone is 12cm and the ratio is 3:2, then the height of the larger cone is 12(3/2) = 18cm.
If the scale factor is 3:2, the ratio of any area measurements between the two cones is the square of that, 9:4. So if the surface area of the smaller cone is 124 cm^2, then the surface area of the larger cone is 124(9/4) = 279 cm^2.
|
|
|
