Question

Cone B has a diameter of 12 kilometers and a slant height of 10 kilometers. Determine the volume of Cone B.

Answer 1

V = 1/3 x PI x r^2 x sqrt(l^2-r^2)

r = 12/2 = 6
l = 10

1/3 x 3.14 x 6^2 x sqrt(10^2-6^2)

volume = 301.59 cubic km (round answer as needed)

Answer 2

`96\pi \text{ square km}`

Explanation:

Since, the volume of a cone is,

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

Where, r is the radius of the cone and h is the height of the cone,

Also, the slant height of the cone is,

`l=√(r^2+h^2)\implies l^2=r^2+h^2\implies h^2=l^2-r^2\implies h = √(l^2-r^2)`

Thus, the volume of the cone can be written as,

`V=(1)/(3)\pi r^2√(l^2-r^2)`

Here, the diameter of the cone = 12 km,

⇒ Radius of the cone, r = Diameter / 2 = 12/2 = 6 km,

And, slant height, l = 10 km,

Thus, the volume of the given cone,

`V=(1)/(3)(\pi)(6)^2(√(10^2-6^2))`

`=(1)/(3)* \pi* (√(100-36))`

`=(\pi)/(3)* 36* (√(64))`

`=(288\pi)/(3)`

`=96\pi\text{ square km}`