Question

If the volume of a cone is 30 cubic feet and it has a base area of 15 square feet, what is the height of the cone?A. 2 ftB. 4 ftC. 5 ftD. 6 ft

Answer 1

To solve the exercise let's remember that the volume of a cone is equal to

`V=(\pi r^2h)/(3)=(A_ch)/(3)`

Where r is de radius and h is the height. Note that Ac is the circle's base of the cone. Solving the equation as a function of the height and replacing the information we have from the exercise

`\begin{gathered} (A_ch)/(3)=V \\ A_ch=V3 \\ h=(3V)/(A_c)=(3(30ft^3))/(15ft^2)=(90ft^3))/(15ft^2)=6ft \\ \end{gathered}`

Thus, the height of the cone is 6 ft.The correct answer is D.