Calculate the Volume of Oil in a Half-Full Cylindrical Tank (Radius 100cm, Height 250cm)

Question

A cylindrical tank is half-full of oil. The cylinder has a base radius of 100 cm. The height of the cylinder is 250 cm. 1 litre = 1000 cm³. How many litres of oil are in the tank? Round your answer to the nearest litre.

Accepted Answer

3927 litres

Answer

Step 1: Recall the formula for the volume of a cylinder: $V = \pi r^2 h$, where $r$ is the base radius and $h$ is the total height of the cylinder. Step 2: Substitute the given values ($r=100$ cm, $h=250$ cm) into the formula to find the total volume of the cylinder: $V_{total} = \pi \times (100)^2 \times 250 = \pi \times 10000 \times 250 = 2500000\pi$ cm³. Step 3: Calculate the volume of the oil, since the tank is half-full: $V_{oil} = \frac{1}{2} \times V_{total} = \frac{1}{2} \times 2500000\pi = 1250000\pi$ cm³ ≈ 3926990.82 cm³. Step 4: Convert the volume from cubic centimeters to litres using the conversion factor 1 litre = 1000 cm³: $\text{Volume in litres} = \frac{3926990.82}{1000} ≈ 3927$ litres.