Question

Find the volume of the cone whose base is shown and whose altitude is 8 meters.

Answer 1

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\implies V=\stackrel{base~area}{\pi r^2}\cdot \cfrac{1}{3}\stackrel{height}{h}\\\\ -------------------------------\\\\ \textit{base of this cone}\\\\ B=\stackrel{a~square}{5\cdot 5}+\stackrel{semi-circle}{\frac{\pi r^2}{2}}\implies B=25+\frac{\pi 3^2}{2}\\\\\\ B=\stackrel{square}{25}+\stackrel{semi-circle}{\frac{9\pi }{2}} \\\\\\ \textit{height of this cone is just 8}\\\\ -------------------------------$

$\bf \textit{volume of this cone}\\\\ V=B\cdot \cfrac{1}{3}h\implies V=\left( 25+\cfrac{9\pi }{2} \right)\left( \cfrac{8}{3} \right) \\\\\\ V=\cfrac{200}{3}+\cfrac{3\pi\cdot 4 }{1}\implies V=\cfrac{200}{3}+12\pi$