Question

A water sample shows 0.036 grams of some trace element for every cubic centimeter of water. Hudson uses a container in the shape of a right cylinder with a radius of 7.3 cm and a height of 12.2 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Hudson collected? Round your answer to the nearest tenth.

Answer 1

We have a water that has a concentration of 0.036 grams per cm³ of some trace element.

We have to find how much of this trace element will be in the container with the sample of water.

This amount will be equal to the volume of the container times the concentration of the trace element.

We start by calculating the volume.

The container is a cylinder. Its volume will be the base area times the height.

We can calculate it as:

`\begin{gathered} V=A_bh \\ V=(\pi r^2)h \\ V=\pi(7.3)^2(12.2) \\ V=\pi(53.29)(12.2) \\ V\approx2042.4688\text{ }cm^3 \end{gathered}`

We can multiply this volume by the concentration as:

`\begin{gathered} m=C\cdot V \\ m=0.036\text{ }(g)/(cm^3)\cdot2042.4688\text{ }cm^3 \\ \\ m\approx73.5\text{ }g \end{gathered}`

Answer: 73.5 grams.