Question

The radius and slant height of a cone are 20cm and 5cm respectively. Find its curved surface area.

Answer 1

Hint: Cone is a three-dimensional structure having a circular base where a set of line segments, connecting all of the points on the base to a common point called apex. The surface area of a cone is equal to the curved surface area plus the area of the base: $\pi {{r}^{2}}+\pi Lr$ where r denotes the radius of the base of the cone, and L denotes the slant height of the cone. The curved surface area is also called the lateral area.
Surface area of cone = Area of the base + Curved surface area = $\pi {{r}^{2}}+\pi Lr$

Complete step by step answer:

Let us first interpret the data given in the question,
Radius of cone (r) = 20cm
Slant height of cone (L) = 5cm
Curved surface area of cone (A) = $\pi Lr$
Substituting the values of radius and slant height of the cone in the above formula for curved surface area of a cone, we get
A = $\pi (5)(20)$
Here let us consider the value of $\pi $ as 3.14
$\pi $= 3.14
Substituting the value of $\pi $ in the A = $\pi (5)(20)$, the value of the curved surface area of the cone can be obtained.
$A=(3.14)(5)(20)$
$\Rightarrow A=3.14\times 100$
$\Rightarrow A=314c{{m}^{2}}$

Therefore curved surface area of cone with radius 5cm and slant height as 20cm is $314c{{m}^{2}}$

Note: In this particular we have been provided with the slant height directly but if the vertical height of the cone(h) is given then the slant height(L) can be found by applying the Pythagoras theorem, i.e ${{L}^{2}}={{h}^{2}}+{{r}^{2}}=>L=\sqrt{{{h}^{2}}+{{r}^{2}}}$ where, r is the radius of the given cone. The total area of the cone can also be calculated which is $\pi {{r}^{2}}+\pi Lr$.