Answer:
To calculate the flow rate, we need to first find the cross-sectional area of the cylinder.
The area ratio is defined as the ratio of the cross-sectional area of the extended cylinder to the cross-sectional area of the cylinder before it was extended.
Let's call the cross-sectional area of the cylinder before it was extended A1, and the cross-sectional area of the extended cylinder A2.
We know that the diameter of the cylinder is 15cm, so the radius is 7.5cm.
The cross-sectional area of a cylinder is given by the formula A = πr^2.
So,
A1 = π(7.5)^2 = 176.71 cm^2
To find A2, we can use the area ratio:
Area ratio = A2/A1 = 0.5
A2 = 0.5 * A1 = 0.5 * 176.71 = 88.36 cm^2
Now we can calculate the flow rate using the formula:
Flow rate = velocity * cross-sectional area
Flow rate = 5 cm/s * 88.36 cm^2 = 441.8 cm^3/s
Therefore, the flow rate is 441.8 cm^3/s.