Question

ms. harrisons science classes use several kinds of cylindrical glassware in their experiments. the table below shows the dimensions of each type of glassware. order the volumes of the pieces of glassware from least to greatest. what is the range in the volumes of the pieces of glassware? round your answer to the nearest whole number. cubic centimeters

Explanation:

Step1: Calculate the volume of each glassware

The formula for the volume of a cylinder is \(V=\pi r^{2}h\).

• Graduated cylinder:

\(r = 1.4\space cm\), \(h=16\space cm\)
\(V_1=\pi\times(1.4)^{2}\times16=\pi\times1.96\times16 = 31.36\pi\approx31.36\times3.14 = 98.4704\space cm^{3}\)

• Test tube:

\(r = 0.9\space cm\), \(h = 12\space cm\)
\(V_2=\pi\times(0.9)^{2}\times12=\pi\times0.81\times12=9.72\pi\approx9.72\times3.14 = 30.5208\space cm^{3}\)

• Petri dish:

\(r = 4.5\space cm\), \(h = 1.5\space cm\)
\(V_3=\pi\times(4.5)^{2}\times1.5=\pi\times20.25\times1.5 = 30.375\pi\approx30.375\times3.14=95.3775\space cm^{3}\)

• Beaker:

\(r = 3.1\space cm\), \(h = 8\space cm\)
\(V_4=\pi\times(3.1)^{2}\times8=\pi\times9.61\times8=76.88\pi\approx76.88\times3.14 = 241.4032\space cm^{3}\)

• Burette:

\(r = 0.7\space cm\), \(h = 70\space cm\)
\(V_5=\pi\times(0.7)^{2}\times70=\pi\times0.49\times70 = 34.3\pi\approx34.3\times3.14=107.702\space cm^{3}\)

Step2: Order the volumes from least to greatest

\(V_2(30.5208)<V_3(95.3775)<V_1(98.4704)<V_5(107.702)<V_4(241.4032)\)
So the order is: test tube, petri dish, graduated cylinder, burette, beaker

Step3: Calculate the range

The range \(R=\text{Max}-\text{Min}\)
\(\text{Max}=V_4 = 241.4032\), \(\text{Min}=V_2=30.5208\)
\(R=241.4032 - 30.5208=210.8824\approx211\)

Answer:

The order from least to greatest: test tube, petri dish, graduated cylinder, burette, beaker.
The range is \(211\) cubic centimeters.