From a square plate with each side 7 cm, squares of area `0.25 cm^(2)` are cut out at each comer and the remaining plate is folded along the cuts to form a cuboid. The volume of this open-top cuboid will be …………. `cm^(3)`.

Options

A. 21
B. 16
C. 18
D. 20

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the dimensions of the square plate
The square plate has each side measuring 7 cm.

### Step 2: Determine the size of the squares cut out from each corner
The area of each square cut out is given as \(0.25 \, \text{cm}^2\). To find the side length of each square, we take the square root of the area:
\[ \text{Side length of each square} = \sqrt{0.25} = 0.5 \, \text{cm} \]

### Step 3: Calculate the dimensions of the remaining plate after cutting
Since squares of \(0.5 \, \text{cm}\) are cut from each corner, the effective dimensions of the remaining plate can be calculated as follows:
- The new length after cutting squares from both ends:
\[ \text{New Length} = 7 \, \text{cm} - 0.5 \, \text{cm} - 0.5 \, \text{cm} = 6 \, \text{cm} \]
- The new breadth after cutting squares from both ends:
\[ \text{New Breadth} = 7 \, \text{cm} - 0.5 \, \text{cm} - 0.5 \, \text{cm} = 6 \, \text{cm} \]

### Step 4: Determine the height of the cuboid
The height of the cuboid formed by folding the remaining plate along the cuts is equal to the side length of the squares cut out:
\[ \text{Height} = 0.5 \, \text{cm} \]

### Step 5: Calculate the volume of the cuboid
The volume \(V\) of a cuboid is given by the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the values we found:
\[ V = 6 \, \text{cm} \times 6 \, \text{cm} \times 0.5 \, \text{cm} = 18 \, \text{cm}^3 \]

### Final Answer
The volume of the open-top cuboid is \(18 \, \text{cm}^3\).

---