Question

The volume of a right circular cone is 9856 cm3

. If the diameter of the base is 28 cm, then

find the slant height of the cone.​

Answer 1

☁Answer:-

Given

volume = 9856m²

Diameter = 28cm

Radius = 28/2 = 14cm.

i.) slant height of cone

l = √[h² + r²]

l = √[(48)² + 14²]

l = √2304 + 196

l = √2500

l = 50 cm.

Therefore , slant height= 50cm

#Hopeithelps

Answer 2

Answer:

Given :-

• Volume of cone = 9856 cm^3
• Diameter = 28 cm
• Radius = d/2 = 28/2 = 14 cm

Volume of a cone = $\frac{1}{3} \pi r^2 h$

Therefore,

$\therefore 9856 cm^3 = \frac{1}{3} \times \frac{22}{7} \times (14)^2 \times h$

$\implies 9856 cm^3 = \frac{1}{3} \times \frac{22}{\cancel{7}} \times \cancel{14} \times 14 \times h$

$\implies 9856 cm^3 = \frac{22 \times 2 \times 14 \times h}{3}$

$\implies 9856 cm^3 = \frac{44 \times 14 \times h}{3}$

$\implies 9856 cm^3 \times 3 = 44 \times 14 \times h$

$\implies h = \frac{9856 \times 3}{44 \times 14}$

$\implies h = \frac{\cancel{9856} \times 3}{44 \times \cancel{14}}$

$\implies h = \frac{704 \times 3}{44}$

$\implies h = \frac{\cancel{704} \times 3}{\cancel{44}}$

$\implies h = 14 \times 3$

$\implies \bf h = 48 cm$

Now,

• h = 48 cm
• r = 14 cm

$\because l^2 = h^2 + r^2$

$\therefore l^2 = 48^2 + 14^2$

$\implies l^2 = 2304 + 196$

$\implies l = \sqrt{2500}$

$\implies \bf l = 50 cm$

Hence, the slant height of the cone is 50 cm.