A rectangular fish tank, 15 m long and 9 m wide, was initially filled with water to its brim. After 5 large containers of water were removed from the fish tank, the tank was ⅔ full. The volume of water in each of the large containers was 45 m³. What was the height of the rectangular fish tank?Height of the rectangular fish tank: ____ m.
Question
A rectangular fish tank, 15 m long and 9 m wide, was initially filled with water to its brim. After 5 large containers of water were removed from the fish tank, the tank was ⅔ full. The volume of water in each of the large containers was 45 m³. What was the height of the rectangular fish tank?Height of the rectangular fish tank: ____ m.
Solution
To solve this problem, we need to find the total volume of the fish tank. We know that after removing 5 large containers of water, each with a volume of 45 m³, the tank was ⅔ full. This means that the volume of water removed represents ⅓ of the total volume of the tank.
Step 1: Calculate the total volume of water removed from the tank. 5 containers * 45 m³/container = 225 m³
Step 2: Since the volume of water removed represents ⅓ of the total volume of the tank, we can find the total volume of the tank by multiplying the volume of water removed by 3. 225 m³ * 3 = 675 m³
So, the total volume of the tank is 675 m³.
Step 3: We know that the volume of a rectangle is given by the formula length * width * height. We can rearrange this formula to solve for height: height = volume / (length * width).
Step 4: Substitute the known values into the formula to find the height. height = 675 m³ / (15 m * 9 m) = 675 m³ / 135 m² = 5 m
So, the height of the rectangular fish tank is 5 meters.
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