The base of a right prism an equilateral triangle of side 8cm and height of the prism is 10 cm. Then the volume of the prism is

Options

A. `320sqrt(3)` cubic cm
B. `160sqrt(3)` cubic cm
C. `150sqrt(3)` cubic cm
D. `300 sqrt(3)` cubic cm

Answer

To find the volume of the right prism with an equilateral triangle as its base, we can follow these steps:

### Step 1: Calculate the area of the base (equilateral triangle)
The formula for the area \( A \) of an equilateral triangle with side length \( a \) is given by:

\[ A = \frac{\sqrt{3}}{4} a^2 \]

In this case, the side length \( a = 8 \) cm.

### Step 2: Substitute the value of \( a \) into the area formula
Substituting \( a = 8 \) cm into the area formula:

\[ A = \frac{\sqrt{3}}{4} \times (8)^2 \]

### Step 3: Calculate \( (8)^2 \)
Calculating \( (8)^2 \):

\[ (8)^2 = 64 \]

### Step 4: Substitute back into the area formula
Now substituting back into the area formula:

\[ A = \frac{\sqrt{3}}{4} \times 64 \]

### Step 5: Simplify the area
Now, simplify \( \frac{64}{4} \):

\[ A = 16\sqrt{3} \text{ cm}^2 \]

### Step 6: Calculate the volume of the prism
The volume \( V \) of the prism is given by the formula:

\[ V = \text{Area of base} \times \text{Height} \]

Given that the height \( h = 10 \) cm, we can substitute the area we found:

\[ V = 16\sqrt{3} \times 10 \]

### Step 7: Calculate the volume
Now, calculate the volume:

\[ V = 160\sqrt{3} \text{ cm}^3 \]

### Final Answer
Thus, the volume of the prism is:

\[ \boxed{160\sqrt{3} \text{ cm}^3} \]