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A right cylindrical tank with circular bases is being filled with water at a rate of 20π cubic meters per hour. As the tank is filled, the water level rises four meters per hour. What is the radius of the tank, in meters? Express your answer in simplest radical form.

Confusedperson  Jun 22, 2018

Best Answer 

 #1
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A right cylindrical tank with circular bases is being filled with water at a rate of 20π cubic meters per hour.

As the tank is filled, the water level rises four meters per hour. What is the radius of the tank, in meters?

Express your answer in simplest radical form.

 

\(\begin{array}{|rcll|} \hline V &=& \pi r^2\cdot h \quad & | \quad : \text{hour} \\\\ \dfrac{V}{\text{hour}} &=& \pi r^2\cdot \dfrac{\text{height}} {\text{hour}} \\\\ 20\pi\dfrac{m^3}{\text{hour}} &=& \pi r^2\cdot 4\dfrac{m}{\text{hour}} \\\\ 20\pi\ m^2 &=& \pi r^2\cdot 4 \quad & | \quad :4\pi \\\\ 5\ m^2 &=& r^2 \\\\ r &=& \sqrt{5}\ m \\ \hline \end{array}\)

 

The radius of the tank is \(\sqrt{5}\) meters

 

laugh

heureka  Jun 22, 2018
 #1
avatar+20011 
+1
Best Answer

A right cylindrical tank with circular bases is being filled with water at a rate of 20π cubic meters per hour.

As the tank is filled, the water level rises four meters per hour. What is the radius of the tank, in meters?

Express your answer in simplest radical form.

 

\(\begin{array}{|rcll|} \hline V &=& \pi r^2\cdot h \quad & | \quad : \text{hour} \\\\ \dfrac{V}{\text{hour}} &=& \pi r^2\cdot \dfrac{\text{height}} {\text{hour}} \\\\ 20\pi\dfrac{m^3}{\text{hour}} &=& \pi r^2\cdot 4\dfrac{m}{\text{hour}} \\\\ 20\pi\ m^2 &=& \pi r^2\cdot 4 \quad & | \quad :4\pi \\\\ 5\ m^2 &=& r^2 \\\\ r &=& \sqrt{5}\ m \\ \hline \end{array}\)

 

The radius of the tank is \(\sqrt{5}\) meters

 

laugh

heureka  Jun 22, 2018

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