A rectangular block of ice measures 40 cm by 25 cm b 15 cm. Find the weight of the block, if ice weights `(9)/(10)` of the weight of the same volume of water and 1 `cm^(3)` of water weights 1 g

Options

A. 9 kg
B. 13.5 kg
C. 8 kg
D. 9.5 kg

Answer

To find the weight of the block of ice, we will follow these steps:

### Step 1: Calculate the Volume of the Ice Block
The volume \( V \) of a rectangular block is given by the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Here, the dimensions of the ice block are:
- Length = 40 cm
- Width = 25 cm
- Height = 15 cm

Substituting the values:
\[ V = 40 \, \text{cm} \times 25 \, \text{cm} \times 15 \, \text{cm} \]
Calculating this:
\[ V = 40 \times 25 = 1000 \, \text{cm}^2 \]
\[ V = 1000 \times 15 = 15000 \, \text{cm}^3 \]

### Step 2: Calculate the Weight of the Same Volume of Water
Since 1 cm³ of water weighs 1 gram, the weight of 15000 cm³ of water is:
\[ \text{Weight of water} = 15000 \, \text{cm}^3 \times 1 \, \text{g/cm}^3 = 15000 \, \text{g} \]

### Step 3: Calculate the Weight of the Ice Block
The weight of ice is \( \frac{9}{10} \) of the weight of the same volume of water. Therefore:
\[ \text{Weight of ice} = \frac{9}{10} \times \text{Weight of water} \]
Substituting the weight of water:
\[ \text{Weight of ice} = \frac{9}{10} \times 15000 \, \text{g} \]
Calculating this:
\[ \text{Weight of ice} = 13500 \, \text{g} \]

### Step 4: Convert the Weight from Grams to Kilograms
To convert grams to kilograms, we divide by 1000:
\[ \text{Weight of ice in kg} = \frac{13500 \, \text{g}}{1000} = 13.5 \, \text{kg} \]

### Final Answer
The weight of the block of ice is **13.5 kg**.

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