Surface Area of Cylinders and Cones from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
Surface area is the total area that covers the surface of a three-dimensional object. For cylinders and cones, the surface area consists of two parts: the curved surface area and the base area. The curved surface area of a cylinder is the area of the side of the cylinder, while the base area is the area of the circular base. The formula to find the curved surface area of a cylinder is 2πrh, where r is the radius of the base and h is the height of the cylinder. The formula to find the base area of a cylinder is πr^2, where r is the radius of the base. To find the total surface area of a cylinder, we add the curved surface area and the base area together. The formula for the total surface area of a cylinder is 2πrh + 2πr^2, or 2πr(h + r). Similarly, for cones, the curved surface area is the area of the side of the cone, while the base area is the area of the circular base. The formula to find the curved surface area of a cone is πrl, where r is the radius of the base and l is the slant height of the cone. The formula to find the base area of a cone is πr^2, where r is the radius of the base. To find the total surface area of a cone, we add the curved surface area and the base area together. The formula for the total surface area of a cone is πrl + πr^2, or πr(l + r). Understanding the surface area of cylinders and cones is important in various real-life situations, such as calculating the amount of paint needed to cover a cylindrical or conical object or determining the amount of material required to wrap a cylindrical or conical package. By applying the formulas for surface area, we can efficiently solve problems involving cylinders and cones in various contexts.
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