Question

Consider the hemi-spherical tank of radius $13m$ as shown in the figure (not drawn to scale). What is the volume of water $\left(in{m}^3\right)$ when the depth of water at the centre of the tank is $6m?$

• A. $78\pi$
• B. $468\pi$
• C. $156\pi$
• D. $396\pi$

Answer 1

The correct option is D $396\pi$

Volume generated by the $Y$ axis revolution equation of circle



$\Rightarrow (x-0{)}^2+(y-13{)}^2={13}^2$
Volume $={\int }_{y_1}^{y^2}{x}^{2}dy$
$=\pi {\int }_0^6(169-(y-13){)}^{2}dy$
$=396\pi$