Question

2 A cone has a volume of 1086 and a base diameter of 12. What is the height of the cone? (1) 27 (3) 3 (2) 9 (4) 4​

Answer 1

well, if its base has a diameter of 12, that means its radius is half that, or 6.

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ V=1086 \end{cases}\implies 1086=\cfrac{\pi (6)^2 h}{3}\implies 3528=36\pi h \\\\\\ \cfrac{3528}{36\pi }=h\implies 31.19\approx h`