Question

7 multiple choice 1 point a spherical container of radius 4 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.) 58.9 58.7 58.8 58.2 58.5

Explanation:

Step1: Calculate volume of sphere

The volume formula for a sphere is $V_s=\frac{4}{3}\pi r^3$. Given $r = 4$ ft, so $V_s=\frac{4}{3}\pi(4)^3=\frac{4}{3}\pi\times64=\frac{256\pi}{3}$ $ft^3$.

Step2: Set up volume - equation for rectangular tub

The volume of a rectangular prism (tub) is $V_r = l\times w\times h$, where $l = 11$ ft, $w = 5$ ft and $h$ is the height (depth) of water we want to find. Since the volume of water in the sphere is equal to the volume of water in the tub, we have $\frac{256\pi}{3}=11\times5\times h$.

Step3: Solve for $h$ in feet

$h=\frac{256\pi}{3\times11\times5}=\frac{256\pi}{165}\approx\frac{256\times3.14}{165}=\frac{803.84}{165}\approx4.87176$ ft.

Step4: Convert feet to inches

Since 1 ft = 12 inches, then $h = 4.87176\times12 = 58.46112\approx58.5$ inches.

Answer:

58.5