A cone-shaped paper cup can hold 35 cubic inches of food. If the radius of the cone is 2.4 inches, what is the height of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth. 5.81 inches 6.57 inches 7.89 inches 8.89 inches

Accepted Solution

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=2.4\\ V=35 \end{cases}\implies 35=\cfrac{\pi (2.4)^2 h}{3}\implies 105=5.76\pi h \\\\\\ \cfrac{105}{5.76\pi }=h\implies 5.805467091295 \approx h\implies 5.81 \approx h[/tex]