Ratio of the heights of two similar cones is 7/9
what is the ratio of their radii? ratio of their volumes??
TIA
If they are similar, the ratio of the radaii is the same.
Now consider that the volume of a cone is 1/3 PI r^2 * h
So the volume ratio will have a (7/9)^2 * 7/9 ratio
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To find the ratio of the radii of two similar cones, we can use the fact that if two cones are similar, their corresponding dimensions (such as height and radius) are proportional.
Given that the ratio of the heights of two similar cones is 7/9, we can set up the proportion:
height of first cone / height of second cone = 7/9
Since the height of a cone is directly proportional to its radius, we can say that the ratio of their radii is the same as the ratio of their heights:
radius of first cone / radius of second cone = 7/9
So, the ratio of their radii is also 7/9.
Now let's calculate the ratio of their volumes. The volume of a cone is given by the formula:
Volume = (1/3) * π * r^2 * h
Using the fact that the ratio of their radii is 7/9, we can substitute the values and simplify the formula:
Volume of first cone / Volume of second cone = (1/3) * π * (7/9)^2 * (7/9)
Simplifying further:
Volume of first cone / Volume of second cone = (49/243) * π
So, the ratio of their volumes is (49/243)π.