Question

a water sample shows 0.086 grams of some trace element for every cubic centimeter of water. dominic uses a container in the shape of a right cylinder with a diameter of 19.2 cm and a height of 13.2 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 dominic collected? round your answer to the nearest tenth.

Explanation:

Step1: Calculate the radius of the cylinder

The diameter \(d = 19.2\) cm. The radius \(r=\frac{d}{2}=\frac{19.2}{2}=9.6\) cm.

Step2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Substitute \(r = 9.6\) cm and \(h=13.2\) cm.
\(V=\pi\times(9.6)^{2}\times13.2=\pi\times92.16\times13.2 = 1216.512\pi\) \(cm^{3}\approx1216.512\times3.14 = 3810.84768\) \(cm^{3}\)

Step3: Calculate the amount of trace element

Since there is \(0.086\) grams of trace element per \(cm^{3}\) of water.
The amount of trace element \(m=0.086\times V\). Substitute \(V = 3810.84768\) \(cm^{3}\)
\(m=0.086\times3810.84768=327.7329\approx327.7\) grams

Answer:

\(327.7\) grams