Height of a prism-shaped part of a machine is 8 cm and its base is an isosceles triangle, whose each of the equal sides 5 cm and remaining side is 6 cm. The volume of the part is

Options

A. 96 cu. cm
B. 120 cu. cm
C. 86 cu. cm
D. 90 cu. cm

Answer

To find the volume of the prism-shaped part of the machine, we will follow these steps:

### Step 1: Identify the dimensions of the isosceles triangle
The base of the prism is an isosceles triangle with:
- Equal sides (a) = 5 cm
- Base (b) = 6 cm

### Step 2: Calculate the area of the isosceles triangle
The area \( A \) of an isosceles triangle can be calculated using the formula:
\[ A = \frac{b}{4} \sqrt{4a^2 - b^2} \]
Substituting the values of \( a \) and \( b \):
\[ A = \frac{6}{4} \sqrt{4 \times 5^2 - 6^2} \]

### Step 3: Simplify the expression
Calculating \( 4 \times 5^2 \):
\[ 4 \times 25 = 100 \]
Now calculate \( 6^2 \):
\[ 6^2 = 36 \]
Now substitute these values back into the area formula:
\[ A = \frac{6}{4} \sqrt{100 - 36} \]
\[ A = \frac{6}{4} \sqrt{64} \]
\[ A = \frac{6}{4} \times 8 \]
\[ A = \frac{48}{4} = 12 \text{ cm}^2 \]

### Step 4: Calculate the volume of the prism
The volume \( V \) of the prism is given by the formula:
\[ V = \text{Area of base} \times \text{Height} \]
Substituting the area of the base and the height:
\[ V = 12 \text{ cm}^2 \times 8 \text{ cm} \]
\[ V = 96 \text{ cm}^3 \]

### Final Answer
The volume of the prism-shaped part of the machine is \( 96 \text{ cm}^3 \).

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