MHB Determining the equation of the volume of a cylinder

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The discussion focuses on determining the volume of a cylinder expressed solely in terms of the radius, r. It clarifies that the standard volume formula involves both radius and height, leading to confusion. One participant suggests that if the cylinder is equilateral, the height can be expressed as twice the radius, allowing for a simplified volume equation. Consequently, the volume can be calculated as V(r) = 2πr³. This approach provides a solution for expressing the volume in terms of radius alone.
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Hi,

My knowledge is not too good and I'm trying to help my son find out how we would go about determining the equation of the volume of the cyclinder V(r), expressed in terms of r alone? We do not know how we would go about this without using l or h?

Any help would be really appreciative (Smile)
 
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bwell said:
Hi,

My knowledge is not too good and I'm trying to help my son find out how we would go about determining the equation of the volume of the cyclinder V(r), expressed in terms of r alone? We do not know how we would go about this without using l or h?

Any help would be really appreciative (Smile)

Since the volume of a cylinder depends both on the radius of the base and its height, either you have misunderstood what you are being asked to do, or have not posted the complete question.

Post the question exactly as worded and any other contextual material which sets up the background for the question.

CB
 
If the cylinder is of an equilateral one, then its diameter is equal to its height, i.e. D=h. But D=2r, so we have h=2r.
Then, the volume of the equilateral cylinder, V(r)=pi(r^2)h=pi(r^2)(2r)=2pir^3.
 
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