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Oxana [17]
1 year ago
6

What is container B that is full after the pumping is complete ?

Mathematics
1 answer:
scoray [572]1 year ago
6 0

<em>Answer</em>

68.4%

<em>Step-by-step explanation</em>

The volume of a cylinder is calculated as follows:

V=\pi r^2h

where <em>r </em>is the radius and <em>h </em>is the height of the cylinder.

In the case of cylinder A, its radius is r = 5 ft (= 10/2) and its height is h = 14 ft. Then, its volume is:

\begin{gathered} V_A=\pi\cdot5^2\cdot14 \\ V_A=350\pi\text{ ft}^3 \end{gathered}

In the case of cylinder B, its radius is r = 8 ft (= 16/2) and its height is h = 8 ft. Then, its volume is:

\begin{gathered} V_B=\pi\cdot8^2\cdot8 \\ V_B=512\pi\text{ ft}^3 \end{gathered}

After the pumping is completed all the liquid in cylinder A, which was full, is placed in cylinder B. If the volume of cylinder B represents 100%, then we need to find what percent, <em>x</em>, represents the volume of cylinder A. We can do this with the help of the next proportion:

\frac{512\pi\text{ ft}^3}{350\pi\text{ ft}^3}=\frac{100\text{ \%}}{x\text{ \%}}

Solving for x:

\begin{gathered} 512\pi\cdot x=100\cdot350\pi \\ x=\frac{100\cdot350\pi}{512\pi} \\ x\approx68.4\text{ \%} \end{gathered}

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