Question

The curved surface area of a right circular cone is 600 cm 2 and its slant height is 30 cm. calculate its capacity.

Answer 1

Solution :-

Curved surface area of right circular cone = πrl

⇒ 600 = (22*r*30)/7

⇒ r = (600*7)/(22*30)

⇒ r = 4200/660

r = 6.36 cm

We know that slant height² = radius² + vertical height² 

⇒ l² = r² + h²

⇒ (30)² = (6.36)² + h²

⇒ 900 = 40.45 + h²

⇒ h² = 900 - 40.45

⇒ h² = 859.55

⇒ h = √859.55

⇒ h = 29.31 cm

Volume of the cone = 1/3*πr²h

⇒ 1/3*22/7*6.36*6.36*29.31

⇒ 26082.71/21

⇒ 1242.03 cm³

Answer.

Answer 2

Answer:

1242.033 cubic cm.

Step-by-step explanation:

Curved surface area of right circular cone = $\pi rl$

Since we are given that The curved surface area of a right circular cone is 600 sq.cm.

Slant height l = 30

$\Rightarrow 600 = \frac{22}{7} \times r \times 30$

$\Rightarrow 600 = \frac{660}{7} \times r$

$\Rightarrow 600 \times  \frac{7}{660} = r$

$\Rightarrow 6.36 = r$

Thus the radius is 6.36 cm

Now , We know that $\text{slant height}^2= radius^2+ height^2$

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

$30^2= 6.36^2+ h^2$

$900= 40.45+ h^2$

$900-40.45= h^2$

$859.55= h^2$

$\sqrt{859.55} = h$

$29.31= h$

Thus the height of cone is 29.31 cm

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

So, volume of given cone=$\frac{1}{3}\times \frac{22}{7} \times 6.36^{2} \times 29.31$

                                          =$1242.033$

Hence the volume of the cone is 1242.033 cubic cm.