Surface Area of a Cylinder

We need to calculate the surface area of the top, base and body. The top and base of the cylinder are both circles which are equal. The area of a circle = πr2 Top and base can be written as: A = (πr2) x 2

If we were to “unwrap” the body of the cylinder, it would be a rectangle. You already know that the area of a rectangle is L X W. In this case the width is the height of the cylinder. The length of the rectangle is actually the circumference of the cylinder. C = πd So: A of the body = πdh

Put the two formula together and the area of a cylinder is: TOP A = (πr2) x 2 + πdh body BASE

Let’s Try It! Find the surface area of the following cylinder. First write out the formula of the area of a cylinder. 10 cm A = (πr2)x2 + πdh Identify the parts of the cylinder that you need for the formula 15 cm d = 20 cm h = 15 cm π = 3.14 r= 10 cm A = 2(πr2) + πdh = 2(3.14)(102) + (3.14)(20)(15) Make the substitutions into the formula and solve.

A = 2(πr2) + πdh = 2(3.14)(102) + (3.14)(20)(15) + 942 Circles Body 1570 cm2

Find the Surface Area of the Cylinder 5 cm 28 cm

A = 2(πr2) + πdh = 2(3.14)(52) + (3.14)(10)(28) + 879.2 1036.2cm

Find the Surface Area of the Cylinder (careful ) 56 cm 22 cm

A = 2(πr2) + πdh = 2(3.14)(282) + (3.14)(56)(22) 4923.52 + 3868.48 8792 cm2