Question

You are laying a concrete border around a circular pond. The pond is 7 metres in diameter and is surrounded by a path 2 metres wide. The concrete needs to be 50 millimetres deep. You are using premixed bagged concrete. 1 cubic metre (m³) requires 106 x 20 kg bags. How many 20 kg bags of premixed concrete do you need? Round your answer to the nearest whole number.

Answer 1

We find the volume of the path in cubic meters and multiply by 106 bags per cubic meter.

The path is an annulus with inner radius r=7 m and outer radius s=7+2=9 m and depth in meters d=50/1000 = 0.05 m.

The volume is the area of the path times its depth; the area is the difference of the area of the outer and inner circles of the annulus.

$V = d(\pi s^2 - \pi r^2) = 0.05 \pi(9^2-7^2) \approx 5.02655 \textrm{ m}^3$

We need

$n \approx 106 \times 5.02655 \approx 532.8$

Answer: 533