Question

27 multiple choice 2 points a spherical container of radius 3 ft is filled with water. the container is then emptied into a rectangular tub with length 11 ft and width 5 ft. when all the water has been transferred, how deep will the water be in the tub? (give your answer in inches and round to the nearest tenth of an inch.)

Explanation:

Step1: Calculate the volume of the spherical container

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\). Given \(r = 3\) ft, we have \(V=\frac{4}{3}\pi(3)^{3}=36\pi\) \(ft^{3}\).

Step2: Calculate the depth of water in the rectangular tub

The volume of water in the rectangular tub is \(V = l\times w\times h\), where \(l = 11\) ft, \(w = 5\) ft. We know \(V=36\pi\) \(ft^{3}\). So \(h=\frac{V}{l\times w}=\frac{36\pi}{11\times5}=\frac{36\pi}{55}\) ft.
Since \(1\) ft \(= 12\) inches, \(h=\frac{36\pi}{55}\times12\) inches.
\(h=\frac{432\pi}{55}\approx\frac{432\times3.14}{55}=\frac{1356.48}{55}\approx24.7\) inches.

Answer:

\(24.7\) inches