# Ratio of Volume of Water to Volume of Conical Tank

Date of Exam:

**Problem**

A conical tank in upright position (vertex uppermost) stored water of depth 2/3 that of the depth of the tank. Calculate the ratio of the volume of water to that of the tank.

A. 4/5 | C. 26/27 |

B. 18/19 | D. 2/3 |

**Answer Key**

[ C ]

**Solution**

$\dfrac{V_\text{air}}{V_\text{tank}} = \left( \dfrac{\frac{1}{3}h}{h} \right)^3$

$\dfrac{V_\text{tank} - V_\text{water}}{V_\text{tank}} = \dfrac{1}{27}$

$27V_\text{tank} - 27V_\text{water} = V_\text{tank}$

$27V_\text{water} = 26V_\text{tank}$

$\dfrac{V_\text{water}}{V_\text{tank}} = \dfrac{26}{27}$ ← *answer*