prism has the base a right angled triangle whose sides adjacent to the right angle are 10 cm and 12 cm long. The height of the prism is 20 cm. The density of the material of the prism is 6 g/cu cm. The weight of the prism is

Options

A. 3.4 kg
B. 4.8 kg
C. 6.4 kg
D. 7.2 kg

Answer

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

### Step 1: Calculate the Area of the Base
The base of the prism is a right-angled triangle with sides of length 10 cm and 12 cm. The area \( A \) of a right-angled triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, we can take the base as 10 cm and the height as 12 cm.

\[ A = \frac{1}{2} \times 10 \, \text{cm} \times 12 \, \text{cm} = \frac{1}{2} \times 120 \, \text{cm}^2 = 60 \, \text{cm}^2 \]

### Step 2: Calculate the Volume of the Prism
The volume \( V \) of the prism can be calculated using the formula:
\[ V = \text{Area of base} \times \text{height} \]
The height of the prism is given as 20 cm.

\[ V = 60 \, \text{cm}^2 \times 20 \, \text{cm} = 1200 \, \text{cm}^3 \]

### Step 3: Calculate the Mass of the Prism
The mass \( m \) of the prism can be calculated using the formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Rearranging this formula gives us:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
The density of the material of the prism is given as 6 g/cm³.

\[ m = 6 \, \text{g/cm}^3 \times 1200 \, \text{cm}^3 = 7200 \, \text{g} \]

### Step 4: Convert Mass to Kilograms
To convert grams to kilograms, we divide by 1000.

\[ \text{Mass in kg} = \frac{7200 \, \text{g}}{1000} = 7.2 \, \text{kg} \]

### Final Answer
The weight of the prism is **7.2 kg**.

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