A solid rectangular piece ofiron measures `1.05mxx70 cm xx1.5 cm`. Find the weight of this piece in kilograms. If `1 cm^(3)` of iron weighs 8 grams.

Answer

To find the weight of the solid rectangular piece of iron, we need to follow these steps:

### Step 1: Convert all measurements to the same unit
The dimensions of the piece of iron are given as:
- Length = 1.05 m
- Width = 70 cm
- Height = 1.5 cm

First, we convert the length from meters to centimeters:
1.05 m = 1.05 × 100 cm = 105 cm

Now, we have:
- Length = 105 cm
- Width = 70 cm
- Height = 1.5 cm

### Step 2: Calculate the volume of the rectangular piece
The formula for the volume \( V \) of a rectangular solid is given by:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]

Substituting the values:
\[ V = 105 \, \text{cm} \times 70 \, \text{cm} \times 1.5 \, \text{cm} \]

Calculating the volume:
\[ V = 105 \times 70 = 7350 \, \text{cm}^2 \]
\[ V = 7350 \times 1.5 = 11025 \, \text{cm}^3 \]

### Step 3: Calculate the weight of the piece of iron
We know that 1 cm³ of iron weighs 8 grams. Therefore, the weight \( W \) can be calculated as:
\[ W = V \times \text{Weight per cm}^3 \]
\[ W = 11025 \, \text{cm}^3 \times 8 \, \text{grams/cm}^3 \]

Calculating the weight:
\[ W = 11025 \times 8 = 88200 \, \text{grams} \]

### Step 4: Convert the weight from grams to kilograms
Since 1 kilogram = 1000 grams, we convert the weight to kilograms:
\[ W = \frac{88200 \, \text{grams}}{1000} = 88.2 \, \text{kg} \]

### Final Answer
The weight of the piece of iron is **88.2 kg**.

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