Question:
Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.
Solution:
It is given that:
Radius of the cone (r) = 6 cm
Height of the cone (h) = 8 cm
Total Surface Area of the Cone (T. S. A) =?
$l^{2}=r^{2}+h^{2}$
$=6^{2}+8^{2}$
= 36 + 64
= 100
l = 10 cm
T. S. A = Curved Surface Area of Cone + Area of Circular Base
$=\pi * r * 1+\pi * r^{2}$
$=(22 / 7 * 6 * 10)+(22 / 7 * 6 * 6)$
$=\frac{1320+792}{7}$
$=301.171 \mathrm{~cm}^{2}$
Therefore the area of the base is $301.71 \mathrm{~cm}^{2}$.