Question

Find the height of a cone with a volume of 464.603 cubic feet and a diameter of 8 feet. ​

Answer 1

we know it has a diameter of 8, thus its radius is half that or namely 4.

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} h=height\\ r=radius\\[-0.5em] \hrulefill\\ r=4\\ V=464.603 \end{cases}\implies 464.603=\cfrac{\pi (4)^2 h}{3} \\\\\\ 3(464.603)=\pi (4)^2 h\implies \cfrac{3(464.603)}{\pi (4)^2}=h\implies 27.73\approx h`

Answer 2

27.75 feet

Explanation:

d = 2r = 8 => r = 4 feet

V = 464.603 = πr²h/3

464.603·3=3.14·16·h =>

h = 1393.809 : 50.24

h ≈ 27.75 feet