__Cylinder__

A cylinder is one of the most basic shapes in geometry. It is formed by taking some fixed origin and rotating it all around with a fixed radius
and from the center take one more base similarly and join with the perpendicular height between the centers of each. So this gives the cylinder.

##
Surface Area of a Cylinder

Surface area of cylinder includes the areas of the top and the bottom surface that is π * r^{2} * r^{2} + π * r^{2} * r^{2}= 2 π * r^{2} * r^{2} and the area of
perimeter that is

( π * r + π * r) h = 2 π * r * h .

##
Volume of the Cylinder

Volume of a cylinder with radius r and height h is given V= π* r^{2} *h.

##
Problems based on Cylinder

**1. Find the surface area of the cylinder with the radius r = 6 cm.**

**Solution:** The surface area of cylinder is 2*π* r^{2} = 2 * π * 6 ^{2} = 226.24 cm^{2}.

**2. Find the surface area of the cylinder with the radius r = 10cm.**

**Solution:** The surface area of cylinder is 2*π* r^{2} = 2 * π * 10^{2} = 628.4 cm^{2}.

**3. Find the volume of the cylinder with radius r= 12 cm and height 30 cm**

**Solution:** The volume of the cylinder is given by 2*π * r*h = 2 * π * 12 * 30 = 2262 cm^{3}.

**4. Find the volume of the cylinder with radius r= 6 cm and height 10 cm**

**Solution:** The volume of the cylinder is given by 2*π * r*h = 2 * π * 6* 10 = 377cm^{3}.

**5. Find the volume of the cylinder with radius r= 2 cm and height 5cm**

**Solution:** The volume of the cylinder is given by 2*π * r*h = 2 * π * 2* 5= 63cm^{3}.

**6. Find the surface area of the cylinder with the radius r = 3cm.**

**Solution:** The surface area of cylinder is 2*π* r^{2} = 2 * π * 3^{2} = 57cm^{2}.

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