Question

for an architecture class, brittany is designing an amazing new aquarium. her favorite feature is the walk - through giant fish tank, where a cylindrical tunnel that visitors can go through is suspended in the middle of the fish tank. the dimensions of her design are below. how many cubic yards of water are needed to fill the fish tank? there is no water in the tunnel. round your answer to the nearest whole number. cubic yards

Explanation:

Step1: Calculate the volume of the rectangular fish - tank

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 18\) yd, \(w=15\) yd, \(h = 12\) yd. So, \(V_{tank}=18\times15\times12\).

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Step2: Calculate the volume of the cylindrical tunnel

The volume formula for a cylinder is \(V=\pi r^{2}h\). The diameter of the cylinder is \(4\) yd, so the radius \(r = 2\) yd, and the height (length) of the cylinder is equal to the width of the tank \(h = 15\) yd. Then \(V_{tunnel}=\pi\times(2)^{2}\times15\).

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Step3: Calculate the volume of water

The volume of water \(V = V_{tank}-V_{tunnel}\).

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Answer:

\(3052\) cubic yards