a water sample shows 0.066 grams of some trace element for every cubic centimeter of water. shandra uses a…

a water sample shows 0.066 grams of some trace element for every cubic centimeter of water. shandra uses a container in the shape of a right cylinder with a radius of 5.7 cm and a height of 13.9 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 shandra collected? round your answer to the nearest tenth.

a water sample shows 0.066 grams of some trace element for every cubic centimeter of water. shandra uses a container in the shape of a right cylinder with a radius of 5.7 cm and a height of 13.9 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 shandra collected? round your answer to the nearest tenth.

Answer

Explanation:

Step1: Calculate cylinder volume

The volume $V$ of a right cylinder is given by $V = \pi r^2 h$. Substitute $r=5.7$ cm and $h=13.9$ cm: $$V = \pi \times (5.7)^2 \times 13.9$$ First compute $(5.7)^2 = 32.49$, then $32.49 \times 13.9 = 451.611$, so $V = \pi \times 451.611 \approx 3.1416 \times 451.611 \approx 1418.7$ cm³.

Step2: Find total trace element

Multiply volume by trace element concentration (0.066 g/cm³): $$\text{Total trace element} = 1418.7 \times 0.066$$ $$= 93.6342$$

Step3: Round to nearest tenth

Round 93.6342 to one decimal place: $$93.6342 \approx 93.6$$

Answer:

93.6 grams