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# Math Examples of Surface, Curves and Equations

• ## How to calculate the total surface area of a cone with a radius of 3cm, height of 4 cm and a length of 5cm?

Cone can be defined as an 3 – D (3 - dimensional) shape whose structure goes from flat and circular base to the vertex (or apex). Actually cone is composed of line segments. These line segments are joined to a single Point in such a way that it forms a Solid structure. This structure contains a circular base and a vertex. Vertex is the top point of the cone. Base is circular that’s why cone has radius. Height of cone is defined as the direct length between the base and vertex.
Figure of cone is shown below.

The total surface area (S) of a cone can be given as sum of area of circular base and area of remaining part. Mathematically,
S = Πr2 + π r l = Π r (r + l) hence
S = Π r (r + l) sq units.
Here length 'l' is given by l = √ (r2 + h2).
Let’s find out how to calculate the total surface area of a cone with a radius of 3cm, height of 4 cm and a length of 5cm. Let’s use the formula to calculate total surface area of cone:
S = Π r (r + l),
Here π = 22 / 7 = 3.14, radius r = 3 cm and length of cone is 5 cm which is given in the problem.
Thus substituting these values in the formula, we get,
S = 3.14 * 3 * (3 + 5) = 3.14 * 3 * 8 = 3.14 * 24 = 75.36 cm2.
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