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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

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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

#1
+18927
+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
+18927
+18
$$\boxed{\mathbf{ V_{\rm{Tank}}=(\pi \cdot r^2)\cdot h } } \small{\text{ \qquad r = 10 ~\rm{m} \qquad V_{\rm{Tank}}=4000 ~\rm{m^3} \qquad \rm{height}_{\rm{of~the~tank}} = h = ~? }} \\\\\\ \begin{array}{rcl} h &=& \dfrac{ V_{\rm{Tank}} } {\pi \cdot r^2}\\\\ h &=& \dfrac{ 4000 ~\rm{m^3} } {\pi \cdot (10 ~\rm{m})^2}\\\\ h &=& \dfrac{ 4000 ~\rm{m^3} } {\pi \cdot 100 ~\rm{m}^2}\\\\ h &=& \dfrac{ 40\not{0}\not{0} ~\rm{m^3} } {\pi \cdot 1\not{0}\not{0} ~\rm{m}^2}\\\\ h &=& \dfrac{ 40 ~\rm{m^3} } {\pi ~\rm{m}^2}\\\\ h &=& \dfrac{ 40 } {\pi} ~\rm{m}\\\\ h &=& 12.7323954474 ~\rm{m}\\\\ h &\approx& 13 ~\rm{m} \end{array}$$