The volume of a right rectangular pyramid is `220 m^(3)`. What is the height of the pyramid, if the area of its base is `55 m^(2)` ?

Options

A. 8 metre
B. 13.5 metre
C. 12 metre
D. 9 metre

Answer

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

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

Given:
- Volume \( V = 220 \, m^3 \)
- Area of Base \( A = 55 \, m^2 \)
- Height \( h = ? \)

### Step 1: Write the formula for the volume of the pyramid
\[ V = \frac{1}{3} \times A \times h \]

### Step 2: Substitute the known values into the formula
\[ 220 = \frac{1}{3} \times 55 \times h \]

### Step 3: Multiply both sides by 3 to eliminate the fraction
\[ 3 \times 220 = 55 \times h \]
\[ 660 = 55h \]

### Step 4: Divide both sides by 55 to isolate \( h \)
\[ h = \frac{660}{55} \]

### Step 5: Simplify the fraction
\[ h = 12 \]

### Conclusion: The height of the pyramid is
\[ h = 12 \, m \]