Question

A water sample shows 0.081 grams of some trace element for every cubic centimeter of water. Hawa uses a container in the shape of a right cylinder with a radius of 9.8 cm and a height of 18.6 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 Hawa collected? Round your answer to the nearest tenth.

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given measures

`\begin{gathered} r=9.8cm \\ h=18.6cm \end{gathered}`

STEP 2: Calculate the volume of the cylinder

`\begin{gathered} Volume=\pi r^2h \\ Volume=\pi*9.8^2*18.6=5611.965187cm^3 \end{gathered}`

STEP 3: Find the amount of trace element Hawa has collected

Since the sample contains the same proportion,

`1cm^3=0.081grams`

For 5611.965187 cubic centimeters, we have:

`5611.965187cm^3=x`

By cross multiplication,

`\begin{gathered} x=5611.965187*0.081=454.5691802grams \\ x\approx454.6grams \end{gathered}`

Hence, Hawa has collected approximately 454.6grams of trace elements