Inner diameter of a hemispherical tank is 3m.a)How many litres of water does it hold?b)In what time will the tank fill if water flows at a speed of 1/2 metre per second through a pipe of diameter 2 cm?. Created by Ataraxia. Math

The inner radius of the hemispherical tank is The volume of the hemispherical tank is,Since Hence the tank can hold of water.Here water flows through the pipe of radius at a speed of where the pipe is assumed to be cylindrical in shape. The volume of water flowing through the pipe per unit time is,Hence time taken to fill the tank is,Hence the tank gets filled in nearly

2 metre per second through a pipe of diameter 2 cm?...

biligiri

The inner radius of the hemispherical tank is $\sf{r=\dfrac{3}{2}\ m.}$

The volume of the hemispherical tank is,

$\longrightarrow\sf{V=\dfrac{2}{3}\,\pi r^3}$

$\longrightarrow\sf{V=\dfrac{2}{3}\,\pi\left(\dfrac{3}{2}\right)^3}$

$\longrightarrow\sf{V=7.069\ m^3}$

Since $\sf{1\ m^3=1000\ L,}$

$\longrightarrow\sf{\underline{\underline{V=7069\ L}}}$

Hence the tank can hold $\bf{7069\ L}$ of water.

Here water flows through the pipe of radius $\sf{r'=1\ cm=0.01\ m}$ at a speed of $\sf{v=\dfrac{1}{2}\ m\,s^{-1},}$ where the pipe is assumed to be cylindrical in shape.