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

Answer:

$96\pi \text{ square km}$

Step-by-step explanation:

Since, the volume of a cone is,

$V=\frac{1}{3}\pi(r)^2h$

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

Also, the slant height of the cone is,

$l=\sqrt{r^2+h^2}\implies l^2=r^2+h^2\implies h^2=l^2-r^2\implies h = \sqrt{l^2-r^2}$

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

$V=\frac{1}{3}\pi r^2\sqrt{l^2-r^2}$

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,

$V=\frac{1}{3}(\pi)(6)^2(\sqrt{10^2-6^2})$

$=\frac{1}{3}\times \pi\times (\sqrt{100-36})$

$=\frac{\pi}{3}\times 36\times (\sqrt{64})$

$=\frac{288\pi}{3}$

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