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The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?

Respuesta :

meerkat18
It is said that the area of the base of the pyramid and that of the cone are equal. In this case, the are a of the square base is s^2 while the area of circle is pi r^2. Hence, s = sqrt pi * r. The volume of the pyramid has a formula of 1/3 bh. h is equal to 3r. Hence, V =  1/3 bh = 1/3 pi r^2 * 3r =  pi r^3. 

The  expression for the volume of the pyramid in terms of the radius r of the cone is πr³

How to find the volume of a pyramid?

volume of a pyramid = 1 / 3 Bh

where

  • B = base area
  • h = height of the pyramid

The height of the pyramid in the diagram is three times the radius of the cone.

Therefore,

3r = h

Hence, the  expression for the volume of the pyramid in terms of the radius r of the cone is as follows:

volume of pyramid = 1 / 3 × B × 3r

volume of pyramid = rB

Where

B = πr²

Therefore,

volume of pyramid = πr³

learn more on pyramid and cone here: https://brainly.com/question/12903285

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