Final answer:
To find the height of the cylindrical tank, calculate its volume using the formula V = πr²h, where r is the radius and h is the height. Then solve for the height by dividing the desired volume by the product of π, the radius squared, and round to the nearest centimeter.
Step-by-step explanation:
To find the height of the cylindrical tank, we need to calculate its volume first. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. We are given that the diameter (2r) of the tank is 73 cm, so the radius (r) is half of that, which is 36.5 cm. We want the volume to be 300 liters, which is equal to 300,000 cm³ (since 1 L = 1000 cm³).
Substituting the values into the formula, we get 300,000 cm³ = 3.142 * (36.5 cm)² * h. Solving for h, we divide both sides of the equation by (3.142 * (36.5 cm)²), resulting in h = 300,000 cm³ / (3.142 * (36.5 cm)²).
Calculating this expression gives us approximately h = 70.91 cm. Since we are asked to round the answer to the nearest centimeter, the height of the tank must be approximately 71 cm.