a cylindrical tank with diameter 2.0m and height 3.2m is to be filled with water. how many litres of water are needed to fill the tank? 100cm3 = 1L
switch to cm from the beginning
2 m = 200 cm, and 3.2 m = 320 cm
volume = π(100^2)(320)
= 3,200,000 cm^3
= 3200π L or appr 10053 L
To find the number of liters of water needed to fill the cylindrical tank, we first need to calculate the volume of the tank in cubic centimeters (cm³), and then convert it to liters (L).
The volume of a cylinder can be calculated using the formula:
Volume = π * (radius)² * height
Given the diameter of the tank is 2.0m, the radius (r) can be calculated by dividing the diameter by 2:
radius = diameter / 2 = 2.0m / 2 = 1.0m
The height of the tank is given as 3.2m.
Now, let's calculate the volume of the tank in cm³:
Volume = π * (1.0m)² * 3.2m
To convert meters (m) to centimeters (cm), we need to multiply by 100:
Volume = π * (1.0m * 100cm/m)² * 3.2m * 100cm/m
Simplifying the equation:
Volume = 3.14 * (100cm)² * 3.2 * 100cm
Volume = 3.14 * 10,000cm² * 320cm
Volume = 3.14 * 3,200,000cm³
Now we have the volume of the cylindrical tank in cm³. To convert it to liters, we need to divide by 1000 since 100 cm³ is equal to 1L:
Volume in liters = (3.14 * 3,200,000cm³) / 1000
Volume in liters = 10,048,000cm³ / 1000
Volume in liters = 10,048L
Therefore, approximately 10,048 liters of water are needed to fill the tank.