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The ratio of the heights of similar cones is 5:2. If the base area of the small cone is 64pi cm^2, find the base area of the large cone. Thanks!

The Ratio Of The Heights Of Similar Cones Is 52 If The Base Area Of The Small Cone Is 64pi Cm2 Find The Base Area Of The Large Cone Thanks class=

Sagot :

Answer: 400π

Explanation:

From the information given, the ratio of the heights is 5:2. This means that the scale factor is 5:2. This means that the ratio of the areas is

(5/2)^2 = 25/4 = 25:4

Thus,

base area of large cone/base area of small cone = 25/4

Given that base area of small cone is 64π, it means that

base area of large cone/64π = 25/4

By cross multiplying,

base area of large cone = 25/4x 64π

base area of large cone = 400π

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