Question

The height h of the cylinder equals to the circumference of the cylinder. Then what is the volume of cylinder in terms of h?

Answer 1

The volume of the cylinder is h^3 / 4π.

Step-by-step explanation:

Let height of the cylinder be = h

Radius of the cylinder be = r

Height =  circumference of the cylinder

       h  = 2πr

      r = h / 2π

Volume of cylinder = πr^2h

                                = π( h / 2π )^2 h

                             V = π x h^2 /  4π^2 x 4 = h^3 / 4π

Thus the volume of the cylinder is h^3 / 4π.

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Answer 2

Answer:

circumference = height

2πr = h

r=  $\frac{h}{2\pi }$

∴Volume= $\pi r^{2} h$ × $\frac{h}{2\pi }$ × $\frac{h}{2\pi }$ × h= $\frac{h^{3} }{4\pi }$