A rectangular tank measures 30cm by 15 cm by 20 cm. It contains water to a depth of 15 cm. How many metal cubes of edge 5 cm need to be placed in the water to raise the water level to the brim of the tank?

Well, it seems like we have a little project on our hands! Let's dive in, shall we?

To find out how many metal cubes we need, let's first calculate the volume of the tank. The formula for volume is length times width times height. So, the volume of the tank is 30 cm × 15 cm × 20 cm, which equals 9,000 cubic centimeters.

Next, we need to determine how much water is already in the tank. The water has a depth of 15 cm, so the volume of water is 30 cm × 15 cm × 15 cm, which equals 6,750 cubic centimeters.

To reach the brim of the tank, we need to add enough water to fill the remaining space. That is, the difference between the total volume of the tank and the volume of water already present. So, 9,000 cubic centimeters - 6,750 cubic centimeters equals 2,250 cubic centimeters.

Now, we know that each metal cube measures 5 cm on each side, so its volume is 5 cm × 5 cm × 5 cm, which equals 125 cubic centimeters.

Finally, we divide the volume of the remaining space by the volume of each metal cube: 2,250 cubic centimeters ÷ 125 cubic centimeters, which equals 18.

So, you'll need 18 metal cubes to raise the water level to the brim of the tank. Happy building!

To solve this problem, we can calculate both the volume of the water already in the tank and the volume of each metal cube. Then, we can compare the two volumes to determine how many cubes are needed.

First, let's calculate the volume of the water already in the tank. The formula for the volume of a rectangular prism (like a tank) is length × width × height. In this case, the length is 30 cm, the width is 15 cm, and the height (or depth of the water) is 15 cm. So the volume of the water is:

Volume_water = length × width × height
Volume_water = 30 cm × 15 cm × 15 cm
Volume_water = 6750 cm³

Next, let's calculate the volume of each metal cube. Since the edge length of the cube is 5 cm, we can use the formula for the volume of a cube, which is edge length × edge length × edge length:

Volume_cube = edge length × edge length × edge length
Volume_cube = 5 cm × 5 cm × 5 cm
Volume_cube = 125 cm³

Now, we can determine how many metal cubes are needed to raise the water level to the brim of the tank. The difference between the volume of the water already in the tank and the volume of the tank itself will be equal to the volume of the cubes:

Volume_cubes_needed = Volume_water_at_brim - Volume_water
Volume_cubes_needed = tank_volume - Volume_water
Volume_cubes_needed = (30 cm × 15 cm × 20 cm) - 6750 cm³
Volume_cubes_needed = 9000 cm³ - 6750 cm³
Volume_cubes_needed = 2250 cm³

Finally, we can calculate how many cubes are needed by dividing the required volume by the volume of each cube:

Number_of_cubes_needed = Volume_cubes_needed / Volume_cube
Number_of_cubes_needed = 2250 cm³ / 125 cm³
Number_of_cubes_needed = 18 cubes

Therefore, you would need 18 metal cubes with an edge length of 5 cm each in order to raise the water level to the brim of the tank.

(30*15*20 - 30*15*15)/5^3 = 18

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