Question

a pile of 6 tons of salt is in the shape of a cone. a contractor is designing a cylindrical storage container with the same diameter and height as the cone. how much salt will the new container hold? the new container will hold tons of salt when full.

Explanation:

Step1: Recall volume formulas

The volume formula for a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$, and for a cylinder is $V_{cylinder}=\pi r^{2}h$.

Step2: Compare volumes

If a cylinder and a cone have the same radius $r$ and height $h$, then $V_{cylinder}=3V_{cone}$.

Step3: Calculate amount of salt

Since the mass of salt is proportional to volume and the volume of the cylinder is 3 - times the volume of the cone, if the cone - shaped pile has 6 tons of salt, the cylinder with the same diameter and height will hold $3\times6 = 18$ tons of salt.

Answer:

18