Which pipe configuration can deliver more water to presidents one 8 cm pipe or two 4cm pipes? Show your work and explain your reasoning.
the larger pipe can carry twice the volume of the two smaller pipes
the cross sectional area is proportional to the square of the radius
smaller pipes ... 2 * (π * 2^2) = 8 π
larger pipe ... π * 4^2 = 16 π
To determine which pipe configuration can deliver more water, we need to compare the flow rates of each configuration. The flow rate of a pipe is determined by its cross-sectional area.
First, let's calculate the cross-sectional area of each pipe:
- The area of the 8 cm pipe can be calculated using the formula for the area of a circle: A = πr², where r is the radius. Since the diameter of the 8 cm pipe is 8 cm, the radius is 4 cm. Therefore, the area of the 8 cm pipe is A = π(4 cm)² ≈ 50.27 cm².
- For the two 4 cm pipes, we need to calculate the combined area. Since we have two pipes, we will multiply the area of one 4 cm pipe by 2. The area of a 4 cm pipe is A = π(2 cm)² ≈ 12.57 cm². Thus, the combined area of the two 4 cm pipes is 2 * 12.57 cm² = 25.14 cm².
Next, we compare the flow rates. The flow rate of a pipe is directly proportional to its cross-sectional area. Therefore, the pipe with the larger cross-sectional area will have a greater flow rate.
In this case, the 8 cm pipe has a larger cross-sectional area compared to the combined area of the two 4 cm pipes. Hence, the 8 cm pipe can deliver more water.
To recap:
- The cross-sectional area of the 8 cm pipe is approximately 50.27 cm².
- The combined cross-sectional area of the two 4 cm pipes is approximately 25.14 cm².
- Therefore, the 8 cm pipe configuration can deliver more water than the two 4 cm pipes.