How to Find the Total Surface Area of a Cylinder: Step-by-Step Guide with Formulas

Area of a Cylinder

To find the area of a cylinder, we need to consider the two main components: the base and the curved surface area

To find the area of a cylinder, we need to consider the two main components: the base and the curved surface area.

1. Base Area: The base of a cylinder is a circle, so we can find its area using the formula for the area of a circle, which is A = πr². Here, “r” represents the radius of the base.

2. Curved Surface Area: The curved surface area of a cylinder can be thought of as unrolling the curved surface and making it flat. It forms a rectangle, where the length is equal to the height of the cylinder (h) and the width is equal to the circumference of the base. The formula to calculate the circumference of a circle is C = 2πr, where “C” is the circumference and “r” is the radius. Therefore, the width of the rectangle is 2πr.

Now, let’s put it all together to find the total area of the cylinder:

Total Surface Area = Base Area + Curved Surface Area

Total Surface Area = (πr²) + (2πrh)

So, the formula to find the total surface area of a cylinder is A = 2πr(r + h), where “A” represents the total surface area, “r” is the radius of the base, and “h” is the height of the cylinder.

It’s important to remember that the units of the radius and height need to be the same for accurate results. Additionally, when calculating the area, make sure to square the value of the radius.

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