Question

Select the correct answer. A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r? A. B. C. D.

Answer 1

(1/12) Pi r^3 option C on plato

Explanation:

r = radius of the cylinder

V = (1/3)Pi c^2 h for a cone.

and c = r/2 and h = u

so Volume of the cone is (1/12) Pi r^3

Answer 2

V =
`(3.14r^3)/(12)`

Explanation:

Volume of Cone =
`\pi r^2 (h)/(3)`

But, Given that radius of cone = r/2 of the cylinder

And,

Height of cone = Radius of cylinder i.e. h = r

Putting this in the above formula.

=> V =
`\pi ((r)/(2) )^2 ((r)/(3))`

=> V =
`(3.14)((r^2)/(4) )((r)/(3) )`

=> V =
`(3.14r^3)/(12)`