Question

plz solve this quickly!
Plz write the answer with explaination.

Answer 1

Given, radius of the circle = 12 cm.

Given, Angle = 120°.

Length of the arc = (θ/360°) * 2πr

⇒ (120/360) * 2 * (22/7) * 12

⇒ 176/7

(i)

Given that is is rolled up to form a cone.

⇒ Radius of the circle R = slant height s = 12 cm.

⇒ length of the arc = Circumference of base of cone = 176/7

Radius of the base of the cone be r.

⇒ 2πr = 176/7

⇒ 2 * (22/7) * r = 176/7

⇒ r = 4 cm.

Height of the cone = √(12)^2 - (4)^2

                                = √144 - 16

                                = √128

                                = 8√2

Volume of cone = (1/3) πr^2h

                           = (1/3) * (22/7) * (4)^2 * 8√2

                           = 189.6 cm^3

Therefore, volume of cone = 189.6 cm^3. - Option (A)

Hope it helps!