Question

at saltwater aquarium works, ms. quinn is filling up three new cylindrical aquariums to put on display. the table below shows the radius and height of each tank. what percent of the total volume of water used by the three aquariums is in the medium tank? round your answer to the nearest percent.

Explanation:

Step1: Calculate the volume of each cylinder

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

• For the small tank: \(r = 8\), \(h=15\). Then \(V_{s}=\pi\times8^{2}\times15=\pi\times64\times15 = 960\pi\)
• For the medium tank: \(r = 12\), \(h = 25\). Then \(V_{m}=\pi\times12^{2}\times25=\pi\times144\times25=3600\pi\)
• For the large tank: \(r = 16\), \(h = 40\). Then \(V_{l}=\pi\times16^{2}\times40=\pi\times256\times40 = 10240\pi\)

Step2: Calculate the total volume

\(V_{total}=V_{s}+V_{m}+V_{l}=960\pi + 3600\pi+10240\pi=(960 + 3600+10240)\pi=14800\pi\)

Step3: Calculate the percentage of the medium - tank volume

The percentage \(P=\frac{V_{m}}{V_{total}}\times100=\frac{3600\pi}{14800\pi}\times100\). Since \(\pi\) cancels out, \(P=\frac{3600}{14800}\times100=\frac{360000}{14800}\approx24.32\)

Answer:

\(24\%\)