A hemispherical tank has a diameter 10cm is fixed by water issuing from a pipe of radius 20cm at 2m per second. Calculate currently to 3.s.f the time in mind Tessa it take to fixed the tank.
you really gotta work on your typing.
volume of tank: π/6 * 10^3 cm^3
fill rate: π*20^2*2 cm^3/s
now divide to get the time.
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To calculate the time it takes to fill the hemispherical tank, we need to determine the volume of water that needs to enter the tank and the rate at which the water enters the tank.
First, let's calculate the volume of the hemispherical tank. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.
Given that the diameter of the tank is 10cm, the radius (r) can be calculated as half of the diameter: r = 10cm / 2 = 5cm. Converting cm to meters, we have r = 5cm / 100 = 0.05m.
Using the formula for the volume of a hemisphere, we find:
V = (2/3)π(0.05m)³
V ≈ 0.0005236 m³
Now, let's determine the rate at which the water enters the tank. The radius of the pipe is 20cm, which is equivalent to 0.2m. The water is issuing from the pipe at a speed of 2m/s. The formula for the volume flow rate is Q = A * v, where A is the cross-sectional area of the pipe and v is the velocity of the water.
The cross-sectional area of the pipe (A) can be calculated using the formula A = πr², where r is the radius of the pipe. Substituting the value of the radius, we get:
A = π(0.2m)²
A ≈ 0.1257 m²
Now, we can calculate the volume flow rate:
Q = 0.1257m² * 2m/s
Q ≈ 0.2514 m³/s
Finally, to calculate the time it takes to fill the tank, we divide the volume of the tank by the volume flow rate:
T = V / Q
T ≈ 0.0005236m³ / 0.2514m³/s
T ≈ 0.00208 s
Rounding this value to 3 significant figures, the time it takes to fill the tank is approximately 0.002 s.