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The volume of a water tank with radius 10m is 4000m3. Calculate the height of the tank to the nearest metre

Guest May 18, 2015

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 #1
avatar+18715 
+18

The volume of a water tank with radius 10m is 4000m3. Calculate the height of the tank to the nearest metre

$$\boxed{\mathbf{
V_{\rm{Tank}}=(\pi \cdot r^2)\cdot h
}
}
\small{\text{$
\qquad r = 10 ~\rm{m} \qquad V_{\rm{Tank}}=4000 ~\rm{m^3}
\qquad \rm{height}_{\rm{of~the~tank}} = h = ~?
$}} \\\\\\
\begin{array}{rcl}
h &=& \dfrac{ V_{\rm{Tank}} } {\pi \cdot r^2}\\\\
h &=& \dfrac{ 4000 ~\rm{m^3} } {\pi \cdot (10 ~\rm{m})^2}\\\\
h &=& \dfrac{ 4000 ~\rm{m^3} } {\pi \cdot 100 ~\rm{m}^2}\\\\
h &=& \dfrac{ 40\not{0}\not{0} ~\rm{m^3} } {\pi \cdot 1\not{0}\not{0} ~\rm{m}^2}\\\\
h &=& \dfrac{ 40 ~\rm{m^3} } {\pi ~\rm{m}^2}\\\\
h &=& \dfrac{ 40 } {\pi} ~\rm{m}\\\\
h &=& 12.7323954474 ~\rm{m}\\\\
h &\approx& 13 ~\rm{m}
\end{array}$$

heureka  May 18, 2015
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1+0 Answers

 #1
avatar+18715 
+18
Best Answer

The volume of a water tank with radius 10m is 4000m3. Calculate the height of the tank to the nearest metre

$$\boxed{\mathbf{
V_{\rm{Tank}}=(\pi \cdot r^2)\cdot h
}
}
\small{\text{$
\qquad r = 10 ~\rm{m} \qquad V_{\rm{Tank}}=4000 ~\rm{m^3}
\qquad \rm{height}_{\rm{of~the~tank}} = h = ~?
$}} \\\\\\
\begin{array}{rcl}
h &=& \dfrac{ V_{\rm{Tank}} } {\pi \cdot r^2}\\\\
h &=& \dfrac{ 4000 ~\rm{m^3} } {\pi \cdot (10 ~\rm{m})^2}\\\\
h &=& \dfrac{ 4000 ~\rm{m^3} } {\pi \cdot 100 ~\rm{m}^2}\\\\
h &=& \dfrac{ 40\not{0}\not{0} ~\rm{m^3} } {\pi \cdot 1\not{0}\not{0} ~\rm{m}^2}\\\\
h &=& \dfrac{ 40 ~\rm{m^3} } {\pi ~\rm{m}^2}\\\\
h &=& \dfrac{ 40 } {\pi} ~\rm{m}\\\\
h &=& 12.7323954474 ~\rm{m}\\\\
h &\approx& 13 ~\rm{m}
\end{array}$$

heureka  May 18, 2015

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