Question

. The radius of a sector is 12 cm and angle is 120°.
By coinciding its straight sides a cone is formed.
Find the volume of that cone.​

Answer 1

Answer:

Step-by-step explanation:

The length or rather the circumference of the arc is the base of the cone formed.

The radius of the sector is the lateral length of of the cone.

We need to get the radius and the height of the cone.

We first get the circumference of the sector as follows :

C = Ф/360 × 2r × π

= 120/360 × 2 × 12 × 3.142 = 25.136 cm

Since this is the base of the cone the Circumference of the circular base = 25.136

C = 2πr

25.136 = 2 × 3.142 × r

r = 25.136 / ( 3.142 × 2)

r = 4 cm

We need to get the height of the cone.

We use pythagorean theorem.

The hypotenuse is the lateral height = radius of the sector

Let h be the height :

h = √(12² - 4²) = 11.31 cm

Volume of a cone = 1/3πr²h

Volume = 3.142 × 1/3 × 4² × 11.31 cm = 189.525 cm³