4. A water tank is a cuboid with dimensions 40 cm by 90 cm by 70 cm . The tank is initially empty and is then filled with the water which flows from a pipe of cross-sectional area $$ 1.2 \mathrm{~cm}^{2} $$ at a speed of $$ 3.5 \mathrm{~m} / \mathrm{s} $$. Calculate the time, in minutes, that it takes to fill the tanks completely.

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To determine the time required to fill the cuboid-shaped water tank completely, we'll follow these steps:

1. **Calculate the Volume of the Tank**:
   
   The tank is a cuboid with dimensions:
   - Length ($$ L $$) = 40 cm
   - Width ($$ W $$) = 90 cm
   - Height ($$ H $$) = 70 cm

$$
   \text{Volume} = L \times W \times H = 40\, \text{cm} \times 90\, \text{cm} \times 70\, \text{cm} = 252{,}000\, \text{cm}^3
   $$
   
   Convert cubic centimeters to cubic meters (since flow rate is in meters per second):
   
   $$
   1\, \text{m}^3 = 1{,}000{,}000\, \text{cm}^3 \implies 252{,}000\, \text{cm}^3 = 0.252\, \text{m}^3
   $$

2. **Determine the Flow Rate of Water from the Pipe**:
   
   The flow rate ($$ Q $$) can be calculated using the formula:
   
   $$
   Q = \text{Area} \times \text{Speed}
   $$
   
   Given:
   - Cross-sectional area of the pipe ($$ A $$) = $$ 1.2\, \text{cm}^2 $$
   - Speed of water ($$ v $$) = $$ 3.5\, \text{m/s} $$
   
   Convert area to square meters:
   
   $$
   1\, \text{cm}^2 = 0.0001\, \text{m}^2 \implies 1.2\, \text{cm}^2 = 0.00012\, \text{m}^2
   $$
   
   Now, calculate the flow rate:
   
   $$
   Q = 0.00012\, \text{m}^2 \times 3.5\, \text{m/s} = 0.00042\, \text{m}^3/\text{s}
   $$

3. **Calculate the Time to Fill the Tank**:
   
   The time ($$ t $$) required to fill the tank is:
   
   $$
   t = \frac{\text{Volume}}{\text{Flow Rate}} = \frac{0.252\, \text{m}^3}{0.00042\, \text{m}^3/\text{s}} = 600\, \text{seconds}
   $$
   
   Convert seconds to minutes:
   
   $$
   600\, \text{seconds} \div 60 = 10\, \text{minutes}
   $$

**Answer:** It takes 10 minutes to fill the tank completely.
It takes 10 minutes to fill the tank completely.

A water tank is a cuboid with dimensions 40 cm by 90 cm by 70 cm .
The tank is initially empty and is then filled with the water which flows
from a pipe of cross-sectional area at a speed of .
Calculate the time, in minutes, that it takes to fill the tanks completely.

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A water tank is a cuboid with dimensions 40 cm by 90 cm by 70 cm . The tank is initially empty and is then filled with the water which flows from a pipe of cross-sectional area at a speed of . Calculate the time, in minutes, that it takes to fill the tanks completely.