Question

derive the formula for volume and surface area of cylinder​

Answer 1

Curved surface Area

The length of the cylinder = the circumference of the base = 2πr. The breadth of the rectangle = Height of the cylindrical can = h. Now, since the rectangular paper was used to wrap the Can firmly, we know that area of rectangle = area of the curved surface of the Cylindrical Can = l × b = 2πr × h

The Curved Surface Area of the Cylinder

= 2πrh

Surface Area

Hence, the total surface area = Area of base 1 +Area of base 2+ Curved surface area = πr2 +πr2 + 2πrh = 2πr2 + 2πrh = 2πr (r+h). Thus,

The Surface Area of a Cylinder = 2πr (r+h)

Volume

we take the product of the base area and height, to get the volume. So, the volume of a cylindrical container = Area of circular base × height = πr2 × h. Therefore,

The Volume of a Cylinder = πr2 h

Answer 2

Formula for volume and surface area of cylinder

Let us considered a cylinder of height = h units and base radius = r units.

Then, we have:

1) Volume of the cylinder = $(\pi \: {r}^{2}h)$ cubic units

2) Curved (lateral) surface area of the cylinder = $(2\pi \: rh)$ sq units

3) Total surface area of the cylinder = $(2\pi {r}h + 2\pi {r}^{2})$ sq units = $2\pi {r}(h+r)$ sq units

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