SOLUTION: If a cylinder has a radius of 3 centimeters and a height of 10 centimeters, calculate its: a. lateral surface area b. total surface area c. Volume

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Lateral surface area = (circumference of the base)*height = square centimeters.
The area of one bases - square centimeters.
The area of both bases = 2*(Area of one base), since they are congruent circles: 2(9pi) = 18pi}}} square centimeters.
Total surface area of a cylinder = Area of the bases + Lateral surface area = square centimeters.
Volume of a cylinder = (area of the base)*height = cubic centimeters.

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FInd the lateral surface area, the total surface area, and the volume of a cylinder whose radius (r) is 3 cm. and whose height (h) is 10 cm.
a) Lateral surface area is:
(Area = Circumference times the height) Substitute r = 3 and h = 10.

This is the exact answer. For an approximation, substitute to get:

sq.cm.
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b) The total surface area of the cylinder is the sum of the lateral surface area (see a) above) and the areas of the top & bottom of the cylinder.
These areas (top & bottom) are the same so you need compute only one and then double it to get both.
Area of the top:
Substitute r = 3.

now double this to include the bottom:

For an approximation, substitute

sq.cm.
Now add this to the lateral surface area () to get:

Exact answer, or approximately:
sq.cm.
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c) The volume of a cylinder is given by:
Substitute r = 3 and h = 10.

or approximately:

cu.cm.