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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.

Jun 22, 2018

#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?

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

The radius of the tank is $$\sqrt{5}$$ meters Jun 22, 2018

#1
+1

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?

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

The radius of the tank is $$\sqrt{5}$$ meters heureka Jun 22, 2018