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The diameter of a cylinder is twice the height (h) of the cylinder. Show that the total surface area of the cylinder is:
[tex]4\pi \ {h}^{2} [/tex]
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The diameter of a cylinder is twice the height h of the cylinder Show that the total surface area of the cylinder istex4pi h2 tex class=

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Answer:

Please check explanations

Step-by-step explanation:

The diameter is twice the height;

if diameter is d and height is h

Then;

d = 2h

But, we know that the radius is half the diameter size. Which means that the diameter is twice the radius

Thus;

2r = 2h

Then r = h

Mathematically the total surface area of a cylinder is;

2pi r (r + h)

substitute h for r

2pi h(h + h)

= 2pi * h * 2h

= 4 pi h^2 (QED)

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