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Surface Area of a Right Circular Cone

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notes

Now the area of each triangle = `1/2` × base of each triangle ×  l
But the curved portion of the figure makes up the perimeter of the base of the cone and the circumference of the base of the cone = 2πr, where r is the base radius of the cone.
So,
Curved Surface Area of a Cone = `1/2 × l × 2πr  = πrl`

where r is its base radius and l its slant height.
Note that `l^2 = r^2 + h^2` (as can be seen from in following fig. by applying Pythagoras Theorem. Here h is the height of the cone.

Therefore, l = `sqrt (r^2 + h^2)`
Now if the base of the cone is to be closed, then a circular piece of paper of radius r is also required whose area is `πr^2`.
So,
Total Surface Area of a Cone = πrl + `πr^2` = πr(l + r) 

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