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Substitution Perimeter Areas of a circle Area of composite shapes Area of a quadrilateral Circumference of a circleHere you will learn about the surface area of a cylinder, including how to calculate the lateral surface area of a cylinder given its radius and its perpendicular height.
Students will first learn about the surface area of a cylinder as part of geometry in th grade.
The surface area of a cylinder is the area that covers the outer surface of a cylinder.
In order to calculate the total surface area of a cylinder you need to find the area of the three parts of the surface and add them together.
There is a lateral surface area and two circular bases.
(The lateral surface area of a cylinder is also referred to as the curved surface area of a cylinder).
is the radius of the cylinder. The lateral surface area of a cylinder is a rectangle.
The circumference of the circle is the length of the rectangle. The height of a cylinder is the height of the rectangle.
Note: The examples on this page are for right circular cylinders. However, the formula above can be used for oblique cylinder if slant height is used for the value of
Let’s look at each part of the surface of a cylinder.
The lateral surface area of a cylinder is a rectangle.
is the formula for the area of the rectangle.
The base of the rectangle is the circumference of the circle:
The height of the rectangle is height of the cylinder given by
To find the area of a rectangle you need to multiply the base by the height
This gives us the formula for the lateral surface area of a cylinder:
Then you need to calculate the area of the base of the cylinder, this is a circle.
Formula for the area of circle:
The area of the top and the area of the base of a cylinder are the same.
So to find the total surface area, you can add the lateral surface area to the area of the two circles:
For example,
Calculate the total surface area of this cylinder with radius of the base and perpendicular height
First, you need to find the lateral surface area of the cylinder:
You then need to find the area of the base of the cylinder:
The area of the top of the cylinder is the same as the area of the base so,
Total surface area:
Since the measurements of the cylinder are in cm, the surface area will be measured in
The surface area of the cylinder is rounded to the nearest tenth.
How does this relate to th grade math?
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DOWNLOAD FREEIn order to calculate the surface area of a cylinder:
Calculate the lateral surface area of the cylinder below, with radius and perpendicular height
Round your answer to the nearest tenth.
This question is only asking us for the lateral surface area, so you only need to find the area of the curved surface that is between the circular bases.
2Add the areas together.
Since you are only calculating the lateral surface area, you do not need to add any other areas.
3Write the answer, including the units.
You need to round the answer to the nearest tenth and include the units – square centimeters.
The lateral surface area of the cylinder is:
Calculate the lateral surface area of the cylinder below, with radius and perpendicular height
Leave your answer in terms of
Calculate the area of each face.
This question is only asking us for the lateral surface area, so you only need to find the area of one face.
Add the areas together.
Since you are only calculating the lateral surface area, you do not need to add any other areas.
Write the answer, including the units.
You need to leave the answer in terms of and include the units – square inches.
Lateral surface area =
Calculate the surface area of the cylinder below, with radius and perpendicular height
Round your answer to the nearest whole.
Calculate the area of each face.
This question is asking us for the total surface area of the cylinder. You need to find the area of each face and add them together.
The top face is the same as the bottom face, so the area of the top is also
Add the areas together.
The sum of the areas is
Write the answer, including the units.
You need to round to the nearest whole number and include units.
The total surface area of the cylinder is:
Calculate the surface area of the cylinder below.
Round your answer to the nearest whole number.
Calculate the area of each face.
This question is asking us for the total surface area of the cylinder. You need to find the area of each face and add them together.
Add the areas together.
The sum of the areas is
Write the answer, including the units.
You need to round to the nearest whole number and include units.
The TOTAL surface area of the cylinder is:
Calculate the surface area of the cylinder below.
Leave your answer in terms of
Calculate the area of each face.
This question is asking us for the answer in terms of When calculating the area of each face, you need to leave the answers in terms of
Add the areas together.
The sum of the areas is
Write the answer, including the units.
You need to leave the answer in terms of and include the units.
The TOTAL surface area of the cylinder is:
Calculate the surface area of the cylinder below.
Leave your answer in terms of
Calculate the area of each face.
This question is asking us for the answer in terms of When calculating the area of each face, you need to leave the answers in terms of
Add the areas together.
The sum of the areas is
Write the answer, including the units.
You need to leave the answer in terms of and include the units.
The TOTAL surface area of the cylinder is:
1. Calculate the lateral surface area of a cylinder with the radius of and the perpendicular height of
Round your answer to the nearest whole number.
You are calculating the lateral surface area of a cylinder, so you substitute the values of and into the formula.
2. Calculate the lateral surface area of a cylinder with the radius of and the perpendicular height of
Round your answer to the nearest whole number.
You are calculating the lateral surface area of a cylinder, so you substitute the values of and into the formula.
3. Calculate the lateral surface area of the cylinder below.
Leave your answer in terms of
You are calculating the lateral surface area of a cylinder, so you substitute the values of and into the formula.
4. Calculate the surface area of the cylinder below.
Round your answer to the nearest whole number.
You are calculating the TOTAL surface area of the cylinder, so you find the area of each face and add them together.
Total surface area:
Surface area (rounded to the nearest whole number)
5. Calculate the TOTAL surface area of the cylinder below.
Round your answer to the nearest whole number.
You are calculating the TOTAL surface area of a cylinder, so you find the area of each face and add them together.
Total surface area:
Surface area (rounded to the nearest whole number)
6. Calculate the TOTAL surface area of the cylinder below.
Leave your answer in terms of
You are calculating the TOTAL surface area of a cylinder, so you find the area of each face and add them together.
Total surface area:
To find the volume of a cylinder, find the area of the base, a circle and multiply it by the height. You can do this with the formula The total surface area is found by adding the area of the two bases and the lateral side.
The lateral side is measured by the height of the cylinder and the circumference of the circle. You can use the surface area of a cylinder formula to solve for any cylinder.
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