The volume of a right circular cone is $9856 \mathrm{~cm}^{3}$. If the diameter of the base is $28 \mathrm{~cm}$. Find:
(a) Height of the cone
(b) Slant height of the cone
(c) Curved surface area of the cone
(a) It is given that diameter of the cone (d) = 28 cm
Radius of the cone(r) = d/2
= 28/2 = 14cm
Height of the cone = ?
Now,
Volume of the cone $(v)=1 / 3 \pi r^{2} h=9856 \mathrm{~cm}^{3}$
$\Rightarrow 1 / 3 * 3.14 * 14^{2} * h=9856$
$\Rightarrow \mathrm{h}=\frac{9856 * 3}{3.14 * 14 * 14}=48 \mathrm{~cm}$
Therefore the height of the cone is 48 cm
(b) It is given that
Radius of the cone(r) = 14 cm
Height of the cone = 48 cm
Slant height (l) = ?
Now we know that
$I=\sqrt{r^{2}+h^{2}}$
$=\sqrt{14^{2}+48^{2}}=\sqrt{2500}=50 \mathrm{~cm}$
Therefore the slant height of the cone is 50 cm.
(c) Radius of the cone(r) = 14 cm
Slant height of the cone (l) = 50 cm
Curved surface area (C.S.A) = ?
Curved surface area of a cone (C.S.A) = πrl
$=3.14 * 14 * 50=2200 \mathrm{~cm}^{2}$
Therefore curved surface of the cone is $2200 \mathrm{~cm}^{2}$