A hemisphere tank of diameter 10m is filled by water issuing from a pipe of radius 20cm at 2cm GC significant figures, the time is minutes, it take to fill the tank.. Take 3.142
Well, well, well, looks like we have ourselves a tank that's ready for a splish-splash! Let's dive right into the math!
First things first, let's find the volume of our pipe. The radius is given as 20cm, which in significant figures becomes 0.20m (let's keep things consistent). Using the formula for the volume of a cylinder, V = πr^2h, our volume of water per minute is 3.142 * 0.20^2 * 2.00, which comes out to be 0.50256 m^3/min.
Now, onto our hemisphere tank! The diameter is given as 10m, so the radius is 5m. Let's find the volume of the tank using the formula for the volume of a hemisphere, V = (2/3)πr^3. Plugging in our radius of 5m, the volume of the tank is (2/3) * 3.142 * 5^3, which results in 261.6667 m^3.
So, to find the time it takes to fill the tank, we can divide the volume of the tank by the volume of water per minute. 261.6667 m^3 ÷ 0.50256 m^3/min gives us approximately 520.7175 minutes.
Voila! It takes around 520.7175 minutes (or should I say "tank" minutes) to fill up that hemisphere tank. Just remember, patience is key when it comes to filling up water tanks!