Question

The following figure shows a cylindrical tank whose diameter is $3$ times the length of its height. The tank holds approximately $231.5$ cubic meters of fluid. Which of the following answer choices most closely approximates the height of the tank?

• A. $2$ meters
• B. $3$ meters
• C. $4$ meters
• D. $5$ meters

Answer 1

The correct option is B $3$ meters

Volume of a cylinder with radius $r$ and height $h=\pi r^{2}h$
Given, $d=3h$
$\Rightarrow r=\frac{3h}{2}$
Thus, $V=231.5=\frac{22}{7}\times {\left(\frac{3h}{2}\right)}^{2}h$
$\Rightarrow h^3=231.5\times \frac{7}{22}\times \frac{4}{9}=32.74$
We know that $3^3=27$ and $4^3=64$
Thus, height of the cylinder should be approximately $=3$ metres