Question 1062609: The radii of two cones are in the ratio 5:7 calculate
1. Area ratio
2. volume ratio
3. if the volume of the smaller cone is 35cm3, find the volume of the larger one.
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
Sorry, that's not enough information.
You must also know the ratio of the heights of the two cones.
Just knowing the ratio of the radii is not enough.
The problem could be done if you knew the two cones had the
same shape, but you aren't told that.
 
Look at the two cones on the left. The radii (in red) of those two cones are
in the ratio 5:7.
Look at the two cones on the right. The radii of those two cones are
ALSO in the ratio 5:7.
It should now be obvious to you that the ratios of the surface areas
and volumes of the two cones on the left are quite different from the
ratios of the surface areas and volumes of the two cones on the right.
Some cones are tall and skinny, some are short and fat, some are short
and skinny, and some are tall and fat.
If you were only given information about their radii and nothing about
their heights or shapes, then be sure to point this out to your teacher,
for that is NOT enough information to answer the questions.
Edwin
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! if the ratio of the sides of 2 polygons is 5/7, then the ratio of the area of the two polygons is (5/7)^2 and the ratio of the volume of the two polygons is (5/7)^3.
the volume of your smaller polygon is 35 cm^3.
let x be the volume of your larger polygon.
then (5/7)^3 * x = 35
solve for x to get x = 96.04 cm^3.
the surface area of your polygon is divided into two parts.
the formula is equal to pi * r^2 + pi * r * l, where l is the small letter L which represents the slant height.
the ratio of the surface area of the smaller cone is therefore equal to (5/7)^2 * pi * r^2 + (5/7)^2 * pi * r * l.
this formula can be made equivalent to (5/7)^2 * (pi * r^2 + pi * r * l).
if this is correct, then the surface area of the smaller cone should be equal to (5/7)^2 * the surface area of the larger cone.
i tested this out with an online calculator and determined that it is correct.
you can do the same, using the following online calculator.
http://ncalculators.com/area-volume/cone-calculator.htm
note that the calculator used the formula pi * r^2 + pi * r * sqrt(r^2 + h^2).
this is because l is equal to sqrt (r^2 + h^2), therefore, they just replace l with sqrt(r^2 + h^2).
the calculator confirms thqt the volume of the smaller cone is equal to (5/7)^3 * the volume of the larger cone, and it confirms that the surface area of the smaller cone is equal to (5/7)^2 * the area of the large cone.
i used the following measurements when testing.
radius of smaller cone is 5.
height of smaller cone is 10.
radius of larger cone is 7.
height of larger cone is 14.
you can see that the ratio of the corresponding sides are (5/7).
you can use whatever measures you see fit.
just make sure that the corresponding sides of the smaller cone are equal to 5/7 * the corresponding sides of the larger cone.
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