A tank with a circular base is 7 m high and 1 m in diameter. The water level is 3 m high.How many more cubic metres of water can the tank hold? Use 3.14 for pi in your calculations and answer to the nearest HUNDREDTH.
Question
A tank with a circular base is 7 m high and 1 m in diameter. The water level is 3 m high.How many more cubic metres of water can the tank hold? Use 3.14 for pi in your calculations and answer to the nearest HUNDREDTH.
Solution
To solve this problem, we first need to calculate the total volume of the tank and then subtract the volume of the water already in it.
Step 1: Calculate the total volume of the tank The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Given that the diameter of the tank is 1 m, the radius (r) is 1/2 = 0.5 m. The height (h) of the tank is 7 m.
So, the total volume of the tank is V = π(0.5 m)²(7 m) = 3.14 * 0.25 m² * 7 m = 5.5 cubic meters.
Step 2: Calculate the volume of the water already in the tank The water level is 3 m high, so we use the same formula but with h = 3 m.
The volume of the water is V = π(0.5 m)²(3 m) = 3.14 * 0.25 m² * 3 m = 2.36 cubic meters.
Step 3: Subtract the volume of the water from the total volume of the tank The tank can hold 5.5 cubic meters - 2.36 cubic meters = 3.14 cubic meters more water.
So, the tank can hold approximately 3.14 more cubic meters of water.
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