Fix the mistake: Changes in Water Depth
Changes in Water Depth ① How Does the Depth Change as Water Is Added to a Container?
When the same amount of water is continuously added to a container with a constant base area (the area of the bottom), the depth increases steadily over time.
🔑 Basics of Changes in Depth
- Volume of water = base area × depth
- If v cm³ of water is added every second, the depth after t seconds = v × t ÷ base area
- A graph of “time and depth” is a straight line (when the base area is constant)
Example 1: Water is added at a rate of 100 cm³ per second to a rectangular container with a base area of 50 cm². What will the depth be after 10 seconds?
Solution:
① Volume of water added = 100 × 10 = 1000 cm³
② Depth = volume ÷ base area = 1000 ÷ 50 = 20 cm
Solution:
① Volume of water added = 100 × 10 = 1000 cm³
② Depth = volume ÷ base area = 1000 ÷ 50 = 20 cm
Example 2: A container with a base area of 30 cm² is filled with water to a depth of 60 cm. If 150 cm³ is drained every second, how many seconds will it take to empty the container?
Solution:
① Volume of water in the container = 30 × 60 = 1800 cm³
② Time = 1800 ÷ 150 = 12 seconds
Solution:
① Volume of water in the container = 30 × 60 = 1800 cm³
② Time = 1800 ÷ 150 = 12 seconds
The same idea applies even if the container is a cylinder. Use “base area = π × r²” to calculate.
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