Question

If the volume of a cone is 168 pi inches and its altitude is 14 inches, what is the radius of the cone? A. 36 inches B. 12 inches C. 72 inches D. 6 inches

Answer 1

The radius of the cone is 6 inches, which i mentioned in option D, for the volume of a cone is 168
`\pi` inches and its altitude is 14 inches.

Explanation:

The given is.

Volume of the cone is 168
`\pi`

Altitude of the cone is 14 inches

Step:1

Formula for Volume of cone is,

`V = \pi r^(2) (h)/(3)`....................................(1)

Where,

V = 168
`\pi` cubic inches

h = 14 inches

Step:2

From the Eqn (1),

168
`\pi` =
`\pi r^(2) (14)/(3)` (∵ Cancel
`\pi` on both sides)

168 =
`r^(2) (14)/(3)`

168 × 3 =
`r^(2) 14`

504 =
`r^(2) 14`

`r^(2)` = 36

r =
`√(36)`

r = 6 inches

Result:

Thus the radius of the cone is 6 inches, If the volume of a cone is 168 pi inches and its altitude is 14 inches.