CSC and BLEPT Math Review Problem 1

Math Problem 1

A cylindrical water tank has a height of 10 meters and a radius of 3 meters. The tank is being filled with water at a rate of 2 cubic meters per minute.

1. Calculate the volume of the tank.
2. Determine how long it will take to fill the tank completely.

Solution:

1. Calculate the volume of the tank:

   The formula for the volume V of a cylinder is:

   V = πr²h

   where r is the radius and h is the height of the cylinder.

   Given:

   r = 3 meters

   h = 10 meters

   So, the volume V is:

   V = π(3)²(10) = π(9)(10) = 90π cubic meters

2. Determine how long it will take to fill the tank completely:

   The tank is being filled at a rate of 2 cubic meters per minute.

   The total volume of the tank is 90π cubic meters.

   To find the time t it takes to fill the tank, we divide the volume of the tank by the rate at which it is being filled:

   t = ^90π⁄₂

   So,

   t = 45π minutes

   Therefore, it will take approximately 45π minutes to fill the tank completely. Approximating π ≈ 3.14159:

   t ≈ 45 × 3.14159 ≈ 141.37 minutes