The number of liters of water needed is 471.24 L.
Step-by-step explanation:
The problem involves finding the amount of water needed to fill a cylinder with a radius of 50 cm and a height of 60 cm. The volume of the cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. The problem also provides information about a metal sphere with a radius of 18 cm and a volume of 24430 cm^3. However, this information is not directly relevant to finding the volume of water needed.
To solve the problem, we first need to calculate the volume of the cylinder that is filled with water. The height of the water is given as 60 cm, and the radius of the cylinder is given as 50 cm. We can substitute these values into the formula for the volume of a cylinder to find the volume of water needed.
Once we have the volume of water in cubic centimeters, we can convert it to liters by dividing by 1000. This gives us the final answer in liters.
Solving:
The volume of the water needed can be calculated by finding the volume of the cylinder that is filled with water, which is given by the formula:
V = πr^2h
where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the water.
Substituting the given values, we have:
V = π(50 cm)^2(60 cm)
V = 471,238.9 cm^3
Since 1 liter is equal to 1000 cm^3, we can convert the volume of water to liters by dividing by 1000:
471,238.9 cm^3 ÷ 1000 cm^3/L = 471.24 L
Therefore, the number of liters of water needed is 471.24 L.