Question

An hourglass composed of two identical cones is 18 cm tall.the radius of each cone is 4cm if you want to fill the bottom half of the hour glass 75% full of salt, how much salt will you need

Answer 1

Check the picture below.

`\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r = 4\\ h = 9 \end{cases}\implies V=\cfrac{\pi (4)^2(9)}{3}\implies V=48\pi \\\\\\ \stackrel{\textit{and 75\% of that will just be }(3)/(4)\textit{ of it}}{48\pi \cdot \cfrac{3}{4}\implies 36\pi \quad \approx \quad 113.097}`