A solid metal cube of side 3 cm is placed in a rectangular tank of dimension 3, 4 and 5 cm. What volume of water can the tank now hold

1. Analyze the question

We are given a rectangular tank with dimensions 3 cm, 4 cm, and 5 cm. A solid metal cube with a side length of 3 cm is placed inside this tank. We need to find the remaining volume available in the tank to hold water after the cube has occupied some of the space.

2. Explain the concept

To solve this, we use the principle of displacement:

• Total Volume of the Tank: The capacity of a rectangular container is calculated as $Length \times Width \times Height$.
• Volume of the Cube: The volume of a cube is calculated as $side^3$ (or $side \times side \times side$).
• Remaining Volume: Once the solid cube is placed inside, it occupies space that water can no longer fill. Therefore, the volume of water the tank can hold is the Total Volume of the Tank minus the Volume of the Cube.

3. Show the solution

Step 1: Calculate the total volume of the rectangular tank.

Step 2: Calculate the volume of the metal cube.

Step 3: Calculate the remaining volume for water.

4. Identify the answer

Comparing our result to the given options: A. 48 cm³ B. 33 cm³ C. 60 cm³ D. 27 cm³

The correct option is B.

5. Tip

When solving geometry problems involving "displacement" (like dropping an object into a container), always remember: Water Volume = Container Volume - Submerged Object Volume. Also, ensure all your units are consistent (in this case, everything is in cm, so the result is correctly in cm³). You've got this!