Cones A and B both have volume cubic 48 π units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B. Explain how you know Cone B has the same volume as Cone A.

The possible dimensions of cone B will be; the radius of 3 units and height of 16 units.

Given information:

Cones A and B both have volume 48 π cubic units, but have different dimensions.

Cone A has a radius of 6 units and a height of 4 units.

It is required to find the possible values of radius and height of cone B.

Let the height of cone B be 16 units.

So, the radius of the cone B will be calculated as,

Therefore, the possible dimensions of cone B will be; the radius of 3 units and height of 16 units.

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A possible solution is that radius of cone B is 2 units and height is 36 units

Step-by-step explanation:

The volume of a cone is given by

where

r is the radius

h is the height

Here we are told that both cones A and B have the same volume, which is:

And

(2)

We also know that cone A has radius 6 units:

and height 4 units:

For cone B, from eq.(2), we get

One possible solution for this equation is

In fact in this case, we get:

Therefore a possible solution is that radius of cone B is 2 units and height is 36 units, and we know that in this case Cone B has the same volume as cone A because it is told by the problem.