A spherical tank of diameter 3m is filled with water from a pipe of radius 30cm at 0.2m/s.calculate an corect to 3s.f the time in minute it take to fill the tank.thankyou godbless
Volume of tank V = 4πradius^3/3
where radius of tank=1.5 m
Pipe radius, r = 0.3 m
pipe length (per second)=0.2 m
Volume per second, v= πr^2*L
Time = V/v in seconds.
Solution
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~Diameter of tank =3m
~Radius of tank is 1.5m
~velocity of water flow in pipe =0.2m/s
~from the velocity of pipe, it is clear that the ~lenght of pipe(L) is 0.2m
~Radius of pipe in meters =0.3m
Time in minutes to fill the tank =(1/60)(volume of tank/volume of pipe)
~volume of tank = (1/3)(4×pi×r×r×r)
=(1/3)(4×(22/7)×1.5×1.5×1.5)
=14.1429m^3/s
~ volume of pipe per second = pi ×r×r×L
=(22/7)×0.3×0.3×0.2
= 0.0566m^3/s
Therefore time in minute to fill the tank =(1/60)(14.1429/0.0566)
=4.16 minutes
A hemispherical tank of diameter 10m is filled by water issuing from a pie of radius 20cm at 2m per second.calculate,correct to three significant figures the time, in minutes,it takes to fill the tank.
17.36 minutes
Well, well, well, it looks like we have a tank that's ready to make a splash! Let's dive right into it, shall we?
First things first, we need to find the volume of that spherical tank. Remember that the formula for the volume of a sphere is (4/3)πr³. In this case, the radius is half the diameter, so it's 3/2 = 1.5m. Now let's crunch some numbers:
Volume of the tank = (4/3)π(1.5)³
≈ 14.13 cubic meters
Now, we need to find the flow rate of the water coming from the pipe. Given that the radius is 30cm (or 0.3m) and the speed is 0.2m/s, we can calculate the flow rate using the formula Q = A × V, where A is the cross-sectional area and V is the velocity:
Flow rate = π(0.3)² × 0.2
≈ 0.0565 cubic meters per second
And now for the grand finale! To find the time it takes to fill the tank, we can simply divide the tank's volume by the flow rate:
Time = Volume of the tank / Flow rate
≈ 14.13 / 0.0565
≈ 249.64 seconds
Alrighty then, let's convert this time to minutes. There are 60 seconds in a minute, so:
Time in minutes = 249.64 / 60
≈ 4.16 minutes
Round that bad boy to 3 significant figures, and we have our answer:
It takes approximately 4.16 minutes to fill the tank. Ta-da!
To calculate the time it takes to fill the spherical tank, we need to find the volume of the tank and then divide it by the rate at which water is being filled.
1. First, let's find the volume of the tank. The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere.
Given that the diameter of the tank is 3m, the radius (r) is half of the diameter, which is 3m / 2 = 1.5m.
So, the volume of the tank is V = (4/3) * π * (1.5m)³.
Calculating this comes out to be V ≈ 14.137m³ (rounded to 3 decimal places).
2. Now, we need to determine the rate at which water is being filled into the tank. In this case, the rate is given as 0.2m/s.
3. To calculate the time it takes to fill the tank, we divide the volume of the tank by the rate.
Time = Volume / Rate
Time ≈ 14.137m³ / 0.2m/s.
The units (m³) will cancel out, leaving us with the unit of time - seconds.
When we perform this division, we get the time in seconds:
Time ≈ 70.685s.
4. Finally, we can convert the time from seconds to minutes by dividing it by 60 (as there are 60 seconds in a minute).
Time in minutes ≈ 70.685s / 60s/minute.
Time in minutes ≈ 1.178 minutes (rounded to 3 significant figures).
Therefore, it takes approximately 1.178 minutes (to 3 significant figures) to fill the spherical tank.