Question

I’m confused on this one

Answer 1

volume of cone = (1/3)(pi)(r^2)h

r = radius = diameter/2 = 8/2 = 4

h = height = 6

volume = (1/3)(3.14159)(4^2)(6)

volume = 100.53096...

Answer: 100.5 units^3

Answer 2

The volume of a cone is one-third the volume of a cylinder into which the cone would fit, that is: base times height, divided by three: $V=\frac{Bh}{3}$. Since the base is a circle we have: $V=\pi r^{2}\frac{h}{3}$. By Cavalieri's Principle this holds even for slanted cones such as this one.

Thus:

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

$V=\pi (\frac{8}{4})^{2}(\frac{6}{3})$

$V=\pi 4^{2}(2)$

$V=32\pi$

$V\approx 100.5units^{3}$