A cylindrical tank (8ft diameter, 12ft height) is filled at 15 ft³/min. How long to reach 80% capacity?

Answer 1

V = (Area of Base)(Height) = πr²h = π(4 ft)²(12 ft) = 192π ft³

80% capacity = 0.80V = 153.6π ft³

Time it takes to fill the tank to 80% capacity = (153.6π ft³) ÷ (15 ft³ / min) ≈ 32.17 minutes

Answer 2

first you want to compute the total volume of the tank

V = pi * r^2 * h

V = pi * 4^2 * 12

V = 603.19

meaning that 80% capacity here would be

80%(603.19) = 482.55

then if it's filling at 15 cubic feet per minute you can divide

482.55 / 15 = 32.17

meaning that it will take approximately 32.17 minutes to fill the cylindrical tank to 80% of its capacity

Answer 3

1. Find the volume of the tank.
2. Find 80% of the volume of the tank.
3. Find how many minutes are needed to get to the volume calculated in step 2.

Details in the video!

Answer 4

To find how long it will take to fill the cylindrical tank to 80% of its capacity, we need to go through the following steps:

Step 1: Calculate the total volume of the cylindrical tank

The formula for the volume of a cylinder is:

V=πr2hV = \pi r^2 hV=πr2h

Where:

1. rrr is the radius of the cylinder
2. hhh is the height of the cylinder
3. π\piπ is approximately 3.14163.14163.1416

Given:

1. The diameter is 8 feet, so the radius r=82=4r = \frac{8}{2} = 4r=28​=4 feet.
2. The height h=12h = 12h=12 feet.

Substitute these values into the volume formula:

V=π(4)2(12)V = \pi (4)^2 (12)V=π(4)2(12) V=π(16)(12)V = \pi (16)(12)V=π(16)(12) V=192π≈192×3.1416=603.19 ft3V = 192 \pi \approx 192 \times 3.1416 = 603.19 \, \text{ft}^3V=192π≈192×3.1416=603.19ft3

So, the total volume of the tank is approximately 603.19 cubic feet.

Step 2: Calculate 80% of the total volume

To find 80% of the tank’s capacity:

\text{80% of volume} = 0.80 \times 603.19 = 482.55 \, \text{ft}^3

Step 3: Determine the time to reach 80% capacity

We are filling the tank at a rate of 15 cubic feet per minute. To find the time it takes to reach 482.55 cubic feet, use the formula:

Time=Volume to fillRate of filling\text{Time} = \frac{\text{Volume to fill}}{\text{Rate of filling}}Time=Rate of fillingVolume to fill​

Substitute the values:

Time=482.5515≈32.17 minutes\text{Time} = \frac{482.55}{15} \approx 32.17 \, \text{minutes}Time=15482.55​≈32.17minutes