A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete . Each step has a rise of 1/4 m and a tread of 1/2 m ( ss fig ) .Caculate the total valoume of concrete required to build the terrace . [ Hint : volume of concrete required to build the first step ` = 1/4 xx 1/2 xx 50 m^(3)`]

Answer

To calculate the total volume of concrete required to build the terrace, we need to find the volume of one step and then multiply it by the total number of steps.

### Step-by-Step Solution:

1. **Identify the dimensions of one step:**
- Rise (height) of one step = \( \frac{1}{4} \) m
- Tread (depth) of one step = \( \frac{1}{2} \) m
- Length of one step = 50 m

2. **Calculate the volume of one step:**
The volume \( V \) of one step can be calculated using the formula for the volume of a rectangular prism:
\[ V = \text{height} \times \text{depth} \times \text{length} \]
Substituting the values:
\[ V = \frac{1}{4} \times \frac{1}{2} \times 50 \]

3. **Perform the multiplication:**
First, calculate \( \frac{1}{4} \times \frac{1}{2} \):
\[ \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \]
Now, multiply by 50:
\[ V = \frac{1}{8} \times 50 = \frac{50}{8} = 6.25 \text{ m}^3 \]

4. **Calculate the total volume for all 15 steps:**
Since there are 15 steps, the total volume \( V_{total} \) is:
\[ V_{total} = 15 \times 6.25 \]

5. **Perform the final multiplication:**
\[ V_{total} = 15 \times 6.25 = 93.75 \text{ m}^3 \]

### Final Answer:
The total volume of concrete required to build the terrace is \( 93.75 \text{ m}^3 \).

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