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Water is poured into an empty cylindrica...

Water is poured into an empty cylindrical tank at a constant rate. In 10 minutes, the height of the water increased by 7 feet. The radius of the tank is 10 feet. What is the rate at which the water is poured?

A

`11pi//8` cubic feet per minute.

B

`11pi//3` cubic feet per minute.

C

`7pi//60` cubic feet per minute.

D

`70pi` cubic feet per minute.

Text Solution

AI Generated Solution

The correct Answer is:
To find the rate at which water is poured into the cylindrical tank, we can follow these steps: ### Step 1: Calculate the Volume of Water Increased The volume \( V \) of a cylinder is given by the formula: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height. Given: - Radius \( r = 10 \) feet - Height increase \( h = 7 \) feet Substituting the values into the formula: \[ V = \pi (10)^2 (7) = \pi (100) (7) = 700\pi \text{ cubic feet} \] ### Step 2: Determine the Time Interval The time interval during which the water is poured is given as 10 minutes. ### Step 3: Calculate the Rate of Water Poured The rate \( R \) at which water is poured can be calculated by dividing the total volume increased by the time taken: \[ R = \frac{\text{Total Volume}}{\text{Total Time}} = \frac{700\pi}{10} = 70\pi \text{ cubic feet per minute} \] ### Final Answer The rate at which the water is poured into the tank is: \[ \boxed{70\pi} \text{ cubic feet per minute} \] ---
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