The base of a right pyramid is a square of side 40 cm long. If the volume of the pyramid is `8000 cm^(3)`, then its height is :

Options

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Answer

To find the height of the right pyramid with a square base, we can use the formula for the volume of a pyramid:

\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

### Step 1: Calculate the Base Area
The base of the pyramid is a square with a side length of 40 cm. The area of a square is given by:

\[ \text{Base Area} = \text{side}^2 = 40 \, \text{cm} \times 40 \, \text{cm} = 1600 \, \text{cm}^2 \]

### Step 2: Substitute the Known Values into the Volume Formula
We know the volume of the pyramid is 8000 cm³. We can substitute the base area and the volume into the volume formula:

\[ 8000 = \frac{1}{3} \times 1600 \times \text{Height} \]

### Step 3: Solve for Height
To isolate the height, we first multiply both sides of the equation by 3:

\[ 8000 \times 3 = 1600 \times \text{Height} \]

This simplifies to:

\[ 24000 = 1600 \times \text{Height} \]

Next, divide both sides by 1600 to solve for the height:

\[ \text{Height} = \frac{24000}{1600} \]

Calculating the right side:

\[ \text{Height} = 15 \, \text{cm} \]

### Final Answer
The height of the pyramid is **15 cm**.

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