# How find the surface area of a cylinder if you know that the radius=10 cm and the height=17 cm?

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We have cylinder with the radius of the base (r)= 10cm and the height (h)= 17

To find the surface area for the whole cylinder we need to calculate the area of the bases (2 circular baser) and the area of the cylinder

The area of the bases = pi* r^2 (pi=3.14)

= (3.14)*100 = 314 cm^2

But we have 2 bases , then both areas = 2(314)= 628 CM^2

Now we will calculate the surface of the cylinder.

The body of the cylinder is actually a rectangle with length is the height of the cylinder and width is the circumference of the circle.

The circumference of the circle = 2*pi*r= 62.8 cm.

Now the surface area of the rectangle = w*L = 62.8 * 17=1067.6 cm^2

Then the total surface area = 1067.6 + 628 = 1695.6 cm^2

The total surface area of a cylinder is a sum of 2 alike areas, top and bottom and sidea area.

Let's calculate the area of top cyllinder:

A1 = pi*r^2, where r = 10 cm

A1 = 3.14*100 = 314 cm^2

The bottom area will ahve the same value:

A2 = 314 cm^2

The side area is:

A3 = w*L = h*2*pi*r = 17*2*3.14*10 = 34*31.4 = 1067.6 cm^2

The total area of the cylinder is:

**A = A1+A2+A3 = 2*314 + 1067.6 = 1695.6 cm^2**

A cylindeder has 3 surfaces. Top and bottoms are cicular surfaces and a curved surface.

The circular surface face has an area of pir^2 each, where r is the radius of the cylinder.

The curved surface area of the cylinder is 2pirh where h is the height of the cylinder.

So the top surface area = Bottom surface area = pi*r^2 = pi*10^2 cm^2 each.

Curved surface area = 2pirh = 2pi*10*17 = 340pi cm^2

Therefore total area = 100pi+100pi+340p = 540pi = 1696.46 cm^2 nearly.

The area of a cylinder id given by the equation:

Area of cylinder = 2*pi*r^2 + 2*pi*r*h

Where:

r = Radius of cylinder

h = Height of cylinder

Substituting given value of r and h in the equation for are of cylinder we get:

Ara of cylinder = 2*(22/7)*10^2 + 2*(22/7)*10*17

= 4400/7 + 7480/7

= 11880/7 = 1697.14 cm^2