# Find the total surface area of a cylinder whose height is 4 cm & the radius of whose base is 3 cm.

jbsims70 | Middle School Teacher | (Level 1) Adjunct Educator

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First you need to make sure you use the correct formula.  You have the shape of a cylinder and you are looking for the surface area.

The formula for finding the surface area of a cylinder is 2 times pi times radius squared plus 2 times pi times radius times height.

This may sound complicated but once you know what each part of the formula means you can solve any problem looking for the surface area of a cylinder.

Pi comes from the measurement of the circumference (or perimeter) of a circle divided by the diameter of the circle.  It doesn't matter how big or small the circle you still divide the circumference by the diameter.  Mathematicians usually use 3.14 as pi because when you use the formula given for finding pi, it comes out to about 3.14 every time.

The radius is one-half of the diameter of the circle.  The diameter is the measure from one point one the circle another point and the line segment crosses the center of the circle.  The radius is also the measure from a point on a circle to the center of the cirlce.

The first part of the formula: 2 times pi times radius squared comes from finding both the top and bottom of the cylinder.  Both are in the shape of a circle so you have to find the area which is pi times radius squared then multiply it twice (for the top and bottom).

The second part of the formula: 2 times pi times radius times height comes from finding the area around the cylinder.  The height is the height of the cylinder.

Your question is "Find the total surface area of a cylinder whose height is 4 cm & the radius of the base is 3 cm."

List your variables from the formula:  pi, r (radius), h (height)

List your known values for the variables:

pi = 3.14, r = 3, h = 4

Replace the values for the variables:

2 (3.14) (3) (3) + 2 (3.14) (3) (4)

Evaluate using order of operations and you will solve the problem.

devilconsort | Student, Grade 10 | eNotes Newbie

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So the total surface area of a cylinder would be the sum of the areas of the two circular bases of the cylinder, and the side of the cylinder.

Now the two bases are congruent, so their areas are equal. If the radius of the base is 3 cm, then the area of the circle is A = pi * r^2 or pi * 9 or 9pi cm^2.

Double that result to get the combined total area of the two bases, or 18pi cm^2.

Now to find the area of the "side" of the cylinder, you'll need some visualization. Imagine that the bases aren't there, and its just a hollow cylinder with the sides. Cut it on one side, and imagine that its flattened out. It should have the shape of a rectangle, whose height we already know, 4 cm. Now finding the length of the other side is quite simple - its the circumference of the base. The circumference of the base was the length that was just spread out in this form, so C = 2 * pi * r or 6pi cm.

Now, the area of the side of the cylinder is then a simple rectangle area calculation - 6pi cm * 4 cm or 24pi cm^2.

Add the areas of the bases to the area of the side to get your total surface area, and you're done!

24pi cm^2 + 18pi cm^2 = 42pi cm^2

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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The surface area of a cylinder is given by the formula:

`2pirh + 2pir^2`

where r is the radius of the base and h is the height.

We know that the height is 4 cm & the radius of the base is 3 cm. Plugging in these values will give us the answer.

If you have trouble remembering the formula think of the surface area of a cylinder as the area of the two circular bases, and the area of the rectangle that wraps around the whole cylinder.

Yojana_Thapa | Student, Grade 10 | (Level 1) Valedictorian

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Surface area of a cylinder:

the formula is (2*pi*r^2) + (2*pi*r*h)

r= 3

h= 4

(2*3.14*3^2) + (2*3.14*3*4)

56.52 + 75.36

131.88 cm^2

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