Find the surface area of the cylinder whose height is 16 cm and the diameter of the base is 6 cm.

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kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

The surface area of a cylinder is S = 2 π r2 + 2 π r h. This is equal to the area of the circles at the top and bottom, and the circmfrence of the barrel multiplied by its height. The radius of the cylinder is its diameter divided by 2. Since your units are consistent, we don't have to worry about reconciling them.

S = 2 π(6/2)^2 + 2 π (6/2) (16) cm^2

S = 2 π(3) ^ 2 + 2 π (3) (16) cm^2

S = 56.55 + 301.59 cm^2

S = 358.14 cm^2

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

The height h = 16

The diameter = 6

To find the surface area we need to calculate the area of the bases and the area of the side.

The area of the bases = 2 * area of the circle

                                    = 2* ( r^2 *pi )

Given the diameter = 6 ==> r = 3

==> Area of the bases = 2* ( 9*pi) = 56.57 ( approx.)

Now we need to calculate the area of the side:

The area = height * circumference

                = 16 * ( 2*r * pi)

                 = 32* 3 * pi = 301. 7

Then the surface area of the cylinder = 56.57 + 301. 7

                                                           = 358.28 cm^2

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