The diameter of a cylinder is twice the height (h) of the cylinder. Show that the total surface area of the cylinder is: 4\pi \ {h}^(2) ​

Question

The diameter of a cylinder is twice the height (h) of the cylinder. Show that the total surface area of the cylinder is:


`4\pi \ {h}^(2)`
​

Answer 1

Please check explanations

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)