Step 1: Given Information
- Diameter of the top of the cone: \( d = 3.5 \, \text{m} \) - Radius of the top of the cone: \( r = \frac{d}{2} = \frac{3.5}{2} = 1.75 \, \text{m} \) - Height of the cone (depth of the pit): \( h = 12 \, \text{m} \)
Step 2: Formula for the Volume of a Cone
The formula for the volume \( V \) of a cone is: \[ V = \frac{1}{3} \pi r^2 h \] Substituting the known values: \[ V = \frac{1}{3} \pi (1.75)^2 \times 12 \] \[ V = \frac{1}{3} \pi \times 3.0625 \times 12 \] \[ V = \frac{1}{3} \pi \times 36.75 \] \[ V = 12.25 \pi \, \text{m}^3 \] Now, using \( \pi \approx 3.1416 \): \[ V \approx 12.25 \times 3.1416 \, \text{m}^3 = 38.48 \, \text{m}^3 \]
Step 3: Conversion from Cubic Meters to Kiloliters
1 cubic meter (m³) is equivalent to 1 kiloliter (kL). Therefore, the volume in kiloliters is: \[ \text{Capacity} = 38.48 \, \text{kL} \]
The capacity of the conical pit is approximately \( 38.48 \, \text{kL} \).