Among all right circular cones with a slant height of 24, 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. let v be the volume of the cone. what is the objective function in terms of the height of the cone, h?

5571.99

Step-by-step explanation:

We need to use the Pythagorean theorem to solve the problem.

The theorem indicates that,

Once this is defined, we proceed to define the volume of a cone,

Substituting,

We need to find the maximum height, so we proceed to calculate h, by means of its derivative and equalizing 0,

then

We select the positiv value.

We have then,

We can now calculate the maximum volume,

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18