Batching a
concrete base
A machine foundation is only as good as the mix poured into it. You will use ratio, volume and percentages to work out exactly how much concrete to order, how much cement it swallows, and whether the job clears its budget.
The job
Read the spec like an engineerAshfield Engineering is casting a reinforced concrete base for a new 40-tonne press. The base is a rectangular slab, 3.00 m long by 2.00 m wide, and its depth is yours to decide.
- Wet concrete has a density of 2400 kg per m³
- Slab depth must be at least 0.40 m — to carry the press footing
- The press data sheet demands grade C25 or stronger
- Order 5% extra to cover spillage and over-dig
- Client's budget for concrete: £350
Your question: which mix, and what depth, satisfies the strength rule, the depth rule and the budget all at once?
Explore the drawing
Drag, drop and tap — then calculateBuild the mix by dragging sacks into the drum and set the depth on the staff gauge. Equivalent ratios behave identically, which is the whole point of ratio: 2:4:8 and 1:2:4 are the same concrete.
Worked solution
Open one step at a timeTake the 0.45 m deep slab in a 1:2:4 mix and check it properly.
The slab is a cuboid, so volume is length × width × depth.
Keep the units consistent. All three measurements are already in metres, so the answer is in cubic metres.
Density questions are marked on the relationship, not the number. Writing mass = volume × density before you substitute banks the method mark.
A 1:2:4 mix has 1 + 2 + 4 = 7 parts in total.
Check: 925.7 + 1851.4 + 3702.9 = 6480 kg. The parts must add back to the whole.
You cannot buy 0.03 of a bag, so you round up to 38 bags.
This is the classic trap. The calculator says 37.03 and the instinct is to write 37. Ask yourself what the number is for: run short of cement and the pour stops.
£326.03 against a £350 budget — approved, with £23.97 in hand.
Use the multiplier × 1.05 in a single step rather than finding 5% and adding it on. Fewer keystrokes, fewer slips.
Go shallower than 0.40 m and the footing is rejected. Go past roughly 0.48 m and the ready-mix bill breaks the budget.
Choose the richer C30 mix and that ceiling drops to about 0.43 m, because you are paying £128 rather than £115 for every cubic metre. Stronger concrete is not free.
Your turn
Answers checked instantlyA different base measures 2.40 m by 1.80 m by 0.50 m deep. Work out its volume in cubic metres.
That base is poured in a 1:2:4 mix. Using a density of 2400 kg/m³, work out the mass of cement needed, to 1 decimal place.
Cement is delivered in 25 kg bags. How many whole bags must be ordered for that base?
Exam-style question
Full mark schemeA larger base measures 3.50 m by 2.20 m by 0.40 m deep and is poured in a 1:1.5:3 mix costing £128 per m³. Concrete is ordered with 5% extra for waste and has a density of 2400 kg/m³.
Work out the total cost of the concrete, to the nearest pound. The mark scheme also asks for the mass of cement, so find that too.
Mark scheme — 5 marks
- Volume = 3.50 × 2.20 × 0.40 = 3.08 m³ M1 A1
- Volume ordered = 3.08 × 1.05 = 3.234 m³ M1
- Cost = 3.234 × 128 = £413.95 = £414 A1
- Cement: total mass = 3.08 × 2400 = 7392 kg; parts = 1 + 1.5 + 3 = 5.5; cement = 7392 ÷ 5.5 = 1344 kg A1
Accepted answer: £414. The commonest lost mark is applying the 5% to the cost instead of the volume — here it happens to give the same figure, but it will not when a fixed delivery charge is added, so build the habit now.
Produced for EAL engineering learners.
Maps to GCSE Mathematics (9–1) — ratio and proportion, volume of prisms, and percentages.