The volume of a right circular cone is 9856 cm3
Question:

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

Solution:

(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 $2200 \mathrm{~cm}^{2}$