## Among all right circular cones with a slant height of 27, what are the dimensions (radius and height) that maximize the volume of the co

Question

Among all right circular cones with a slant height of 27, what are the dimensions (radius and height) that maximize the volume of the cone? The slant height of a cone is the distance from the outer edge of the base to the vertex.

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Math
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2021-11-23T16:23:29+00:00
2021-11-23T16:23:29+00:00 1 Answer
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## Answers ( )

Answer:Radius = 22.04 unit,Height = 15.58 unitStep-by-step explanation:Since, the volume of cone,

Where,

x = radius,

h = height,

Since, the slant height of a cone is,

Here, l = 27.

So, the volume would be,

Differentiating with respect to x,

For maxima or minima,

But side can not be negative,

So, x = 22.04,

Since,

While,

Thus, by the

first derivative test,V(x) is maximum at x = 22.04,

Also, from equation (1),

h = 15.58

Hence,

for maximising the volume, the radius and height of the cone would be 22.04 unit and 15.58 unit respectively.