A plate on square base made of brass is of length x cm and width 1mm. The plate weighs 4725 gm. If 1 cubic cm of brass weighs 8.4 gram, then the value of x is :

Options

A. 75
B. 76
C. 72
D. 74

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert the width from mm to cm
The width of the plate is given as 1 mm. We need to convert it to centimeters since the length is in centimeters.
- **Conversion**: \(1 \text{ mm} = 0.1 \text{ cm}\)

### Step 2: Calculate the volume of the plate
The volume \(V\) of the plate can be calculated using the formula for the volume of a rectangular prism:
\[ V = \text{length} \times \text{width} \times \text{thickness} \]
Here, the length is \(x\) cm, the width is \(0.1\) cm, and we will denote the thickness as \(t\) (which is also in cm). However, since the thickness is not provided, we will assume it to be negligible for the sake of this calculation.

### Step 3: Relate weight to volume
We know that the weight of the plate is given as 4725 grams. The weight can also be calculated using the density of brass:
\[ \text{Weight} = \text{Volume} \times \text{Density} \]
Given that the density of brass is \(8.4 \text{ g/cm}^3\), we can express the volume in terms of weight:
\[ V = \frac{\text{Weight}}{\text{Density}} = \frac{4725 \text{ g}}{8.4 \text{ g/cm}^3} \]

### Step 4: Calculate the volume
Now, we perform the calculation:
\[ V = \frac{4725}{8.4} \approx 562.5 \text{ cm}^3 \]

### Step 5: Set up the equation for volume
Now we can set up the equation for the volume of the plate:
\[ V = x \times 0.1 \text{ cm} \]
So, we have:
\[ x \times 0.1 = 562.5 \]

### Step 6: Solve for \(x\)
To find \(x\), we rearrange the equation:
\[ x = \frac{562.5}{0.1} = 5625 \text{ cm} \]

### Step 7: Final value of \(x\)
Thus, the value of \(x\) is:
\[ x = 5625 \text{ cm} \]