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| Cylinder Volume and Surface Area |
Cylinder Volume and Surface Area
A cylinder is a 3-dimensional object with a circular base and straight, parallel sides.
To find the volume and surface area, all we need is the radius (r), height (h), and pi (π).
Volume
The volume of a cylinder is calculated by multiplying the area of the base by the height.
Because the base of a cylinder is a circle, we must find the area using the following formula:
Area of a Circle = πr2
We then multiply this by the the height of the cylinder to get the formula for the total area:
Volume = πr2h
Surface Area
The surface area of a cylinder is calculated by adding the area of the base and top to the area of the sides.
Because the base of a cylinder is a circle, we must find the area using the following formula:
Area of a Circle = πr2
Next, we will calculate the surface area of the sides.
Picture a cylinder with paint covering the sides. If we lay the cylinder down onto a piece of paper and roll it one full rotation then pick it up, we will observe a rectangle painted onto the paper. This rectangle would be of equal height to the height of the cylinder, and have a width of the circumference of the base.
We already know that the base of a cylinder is a circle, so we can find the circumference by using the formula:
Circumference of a Circle = 2πr
We can now put this all together to get our surface area formula, but remember that we need to account for both the top and bottom of the cylinder by multiplying the area of the base by 2.
Surface Area = 2πr2 + 2πrh