Question

Verify Eulers formula of cylinder

Answer 1

Euler's formula is V-E+F =2 where V denotes the number of vertices, E denotes number of edges and F denotes number of faces. For cylinder, Faces are the curved part of the cylinder ,the top which is flat , the bottom which is flat.

Answer 2

Euler's formula for a cylinder states that the sum of the areas of the two bases of the cylinder and the lateral surface area is equal to the product of the perimeter of the base and the height of the cylinder.

The formula is: A = $2\pi r^2 + 2\pi rh$

Where A is the total surface area of the cylinder, π is pi, r is the radius of the base, and h is the height of the cylinder.

This formula can be verified by considering the two circular bases of the cylinder, which have an area of $\pi r^2$ each, and the lateral surface area, which is a rectangle that wraps around the cylinder and has a width of 2πr and a height of h. The total area of the rectangle is 2πr*h.

If we add the areas of the two circular bases and the lateral surface area, we get:

$\pi r^2 + \pi r^2 + 2 \pi r*h = 2 \pir^2 + 2 \pi rh$

Which is the same as the formula stated earlier.

Euler's formula can also be verified by considering the perimeter of the base and the height of the cylinder. The perimeter of a circle is 2πr, and the product of the perimeter and the height is 2πr*h which is same as the lateral surface area of the cylinder

Therefore, Euler's formula for the cylinder is verified.

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