Question

you have been asked by your boss to calculate the volume of concrete for 1 circular pier footing. the circular pier footing is 354 mm in diameter and 5 m deep. how many cubic metres of concrete would be required to fill the footing?

• use 3.14 as the value for pi
• answer to two decimal places
• do not use m3 in your answer

Explanation:

Convert diameter to meters

The diameter is given in millimeters.

$$ d = 354\text{ mm} = 0.354\text{ m} $$

Calculate the radius

The radius is half of the diameter.

$$ r = \frac{d}{2} = \frac{0.354\text{ m}}{2} = 0.177\text{ m} $$

Calculate the cross-sectional area

The area of the circular base is calculated using \(\pi \approx 3.14\).

$$ A = \pi r^2 = 3.14 \times (0.177\text{ m})^2 $$

$$ A = 3.14 \times 0.031329\text{ m}^2 \approx 0.09837306\text{ m}^2 $$

Calculate the volume

The volume is the base area multiplied by the depth.

$$ V = A \times h = 0.09837306\text{ m}^2 \times 5\text{ m} \approx 0.4918653\text{ m}^3 $$

Round to two decimal places

Rounding the volume to two decimal places gives:

$$ V \approx 0.49 $$

Answer:

0.49