Question 1155823: The radii of two similar cones are 1.0 and 2.5 respectively. What is the ratio of:
Their lateral areas?
Found 2 solutions by jim_thompson5910, greenestamps:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Answer: 1:6.25
Imagine we had 2 squares. One square is 1 by 1, so its area is 1*1 = 1 suare unit. The second square is 2.5 by 2.5, so its area is 2.5*2.5 = 6.25 square units.
The ratio of the side lengths is 1:2.5, meaning that the second square's side length is 2.5 times longer than the first square's side length.
The ratio of the areas is 1:6.25, meaning the second square's area is 6.25 times that of the first square's area.
The surface area in general follows this idea, so the ratio of surface areas of the two cones is 1:6.25
The same idea applies to the lateral surface areas as well. This is because we can unfold the outer surface (think of peeling off a sticker label) to form the geometric net, which is just a flat 2D shape. That shape has an area, leading to the surface area.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
It's a basic principle for similar figures, no matter how simple or complex they are. It can be two squares (which are all similar to each other), or it can be an entire city and a scale model of that city.
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If two similar figures have a scale factor (ratio of corresponding linear measurements) of a:b, then
(1) the ratio of corresponding area measurements is a^2:b^2; and
(2) the ratio of corresponding volume measurements is a^3:b^3
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Radii are linear measurements; lateral surface areas are area measurements.
Given the ratio of radii is 1:2.5, the ratio of lateral surface areas is 1^2:2.5^2, or 1:6.25.
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