Question

The radius of a of sector O-PQR is 12 cm and angle POQ is equal to 120 degrees .A cone is formed such that radii of OP and OQ coincide.Find the volume of the cone.

Answer 1

Answer:

Volume of cone is 189.33 cubic centimeter.

Step-by-step explanation:

Given radius of a of sector O-PQR is 12 cm and angle POQ is equal to 120 degrees .A cone is formed such that radii of OP and OQ coincide. We have to find the volume of cone.

Length of arc PQ can be calculated as

= $\frac{\theta}{360^{\circ}}\times 2\pi r$

= $\frac{120}{360^{\circ}}\times 2\pi 12$

= $8\pi$

Now, this arc is the circumference of the circle of cone whose radius can be calculated as

$2\pi r=8\pi$ ⇒ r=4 cm

The height of cone can be calculated by the formula

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

⇒ $12^2=4^2+h^2$

⇒ $h^2=144-16=128$ ⇒ h=11.3 cm

Now, Volume of cone=$\pi r^2\frac{h}{3}$

                                   =$3.14\times \frac{16}{3}$

                                   =$189.33cm^3$