自来水管的内直径是 2 厘米，水管内的流速是每秒 8 厘米，一名同学去洗手，走时忘记关水龙头， 4 分钟浪费了（ ）立方厘米的水。
Answer (2)
Calculate the radius of the pipe: r = 2 2 = 1 cm.
Calculate the area of the pipe's cross-section: A = π ( 1 ) 2 = π cm 2 .
Convert the time to seconds: t = 4 × 60 = 240 seconds.
Calculate the volume of wasted water: V = π × 8 × 240 = 1920 π ≈ 6031.86 cm 3 . The amount of water wasted is 6031.86 cm 3 .
Explanation
Problem Analysis First, let's analyze the problem. We are given the inner diameter of a water pipe, the flow rate of water, and the time the water tap was left open. We need to find the volume of water wasted.
Calculate the radius The inner diameter of the water pipe is 2 cm, so the radius is: r = 2 d iam e t er = 2 2 = 1 cm
Calculate the area The area of the cross-section of the water pipe is: A = π r 2 = π ( 1 ) 2 = π cm 2
Convert time to seconds The water tap was left open for 4 minutes, which is: t = 4 minutes = 4 × 60 = 240 seconds
Calculate the volume The volume of water wasted is: V = A × f l o w × t = π × 8 × 240 = 1920 π cm 3 Using π ≈ 3.14159 , we get: V ≈ 1920 × 3.14159 = 6031.85 cm 3
Final Answer Therefore, the volume of water wasted is approximately 6031.86 cubic centimeters.
Examples
Imagine you are a plumber calculating water usage for a household. Knowing the pipe diameter, water flow rate, and duration of use helps estimate total water consumption, which is crucial for billing and resource management. This calculation is also useful in environmental studies to assess water wastage from leaky faucets or open taps, promoting water conservation efforts.
The volume of water wasted from a running tap over 4 minutes is approximately 6031.86 cm³. This is calculated using the pipe's inner diameter, flow rate, and duration the tap was left open. The formula used involves determining the cross-sectional area of the pipe and multiplying by the flow and time.
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