Question

A cylinder of diameter 8cm and unknown height is filled with water. The cylinder starts leaking and the height of water in this cylinder decreases by 0.25cm per minute. What is the rate at which the volume of water is leaking from the cylinder in centimetres per minute, when the level of water is down to 3cm?

Answer 1

The rate at which the volume of water is leaking from the cylinder is 4π cm³/minute when the water level is down to 3cm.

Step-by-step explanation:

To find the rate at which the volume of water is leaking from the cylinder, we need to determine the rate at which the height of water is decreasing.

Given that the height of water is decreasing by 0.25cm per minute, we can calculate the volume of water that is being leaked per minute.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is the height of the cylinder. Since the diameter of the cylinder is 8cm, the radius (r) is half of the diameter, which is 4cm.

Substituting the values into the formula, we have V = π(4cm)^2h = 16πh. Therefore, the rate at which the volume of water is leaking from the cylinder is 16π times the rate at which the height is decreasing.

When the water level is down to 3cm, the rate at which the volume of water is leaking from the cylinder is 16π(0.25cm/minute) = 4π cm³/minute.