Two cubes of sizes 4 cm and 6 cm are melted to form a cuboid of length 10 cm and breadth 8 cm .What is the height of the cuboid so formed ?

Options

A. 4.5 cm
B. 3.8 cm
C. 3.5 cm
D. 2.5 cm

Answer

To find the height of the cuboid formed by melting two cubes of sizes 4 cm and 6 cm, we can follow these steps:

### Step 1: Calculate the volume of the first cube
The volume \( V \) of a cube is given by the formula:
\[ V = \text{side}^3 \]
For the first cube with a side of 4 cm:
\[ V_1 = 4^3 = 64 \text{ cm}^3 \]

### Step 2: Calculate the volume of the second cube
Using the same formula for the second cube with a side of 6 cm:
\[ V_2 = 6^3 = 216 \text{ cm}^3 \]

### Step 3: Calculate the total volume of the two cubes
Now, we can find the total volume by adding the volumes of both cubes:
\[ V_{\text{total}} = V_1 + V_2 = 64 \text{ cm}^3 + 216 \text{ cm}^3 = 280 \text{ cm}^3 \]

### Step 4: Use the volume of the cuboid to find the height
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
We know the length \( L = 10 \text{ cm} \) and breadth \( B = 8 \text{ cm} \). Let the height be \( h \). Thus, we have:
\[ V_{\text{total}} = L \times B \times h \]
Substituting the known values:
\[ 280 \text{ cm}^3 = 10 \text{ cm} \times 8 \text{ cm} \times h \]

### Step 5: Solve for height \( h \)
Now, we can solve for \( h \):
\[ 280 = 80h \]
Dividing both sides by 80:
\[ h = \frac{280}{80} = 3.5 \text{ cm} \]

### Conclusion
The height of the cuboid formed is \( 3.5 \text{ cm} \).

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