Question 1

How do you calculate how much concrete is needed for a slab?

Accepted Answer

Volume (m³) = Length × Width × Thickness. Convert to cubic yards: divide m³ by 0.7646, or divide ft³ by 27. For a 20 ft × 15 ft × 4 in slab: volume = 20 × 15 × (4/12) = 100 ft³ ÷ 27 = 3.7 yd³. ACI 211.1 coverage: 1 yd³ covers approximately 81 ft² at 4 in depth. Always add 5–10% waste.

Question 2

What is the formula for the volume of a cylinder?

Accepted Answer

Volume = π × r² × h, where r is the radius and h is the height. For a round concrete column 0.5 m radius and 3 m tall: V = π × 0.25 × 3 = 2.356 m³. IBC 2021 §1905.1 requires a minimum 200 mm (8 in) diameter for concrete columns. The lateral surface area (formwork) = 2πrh.

Question 3

How do you calculate the area of a trapezoid for a retaining wall?

Accepted Answer

Trapezoid area = ½ × (top width + bottom width) × height. For a retaining wall cross-section 2.4 m top, 1.8 m bottom, 1.2 m height: Area = ½ × (2.4 + 1.8) × 1.2 = 2.52 m². Multiply by wall length for volume. HEC-15 recommends side slopes between 1:1 and 3:1 (H:V) for earthen drainage channels.

Question 4

What is an annulus and when is it used in construction?

Accepted Answer

An annulus is the ring-shaped area between two concentric circles: Area = π(R² − r²), where R is the outer radius and r is the inner radius. Used for: hollow concrete columns, pipe cross-sections (to find wall area), ring footings, and caissons. ACI 318-19 §18.9.2 requires hollow column wall thickness ≥ D/16 (minimum 4 in / 100 mm).

Question 5

How do you calculate the volume of a dome or hemisphere?

Accepted Answer

Hemisphere volume = (2/3)πr³. Full sphere volume = (4/3)πr³. For a hemisphere with 6 m diameter (r = 3 m): V = (2/3) × π × 27 = 56.55 m³. Curved surface area = 2πr² = 56.55 m². A sphere encloses maximum volume for minimum surface area — its volume-to-surface ratio (r/3) is the highest of any shape.

Question 6

What is the formula for a cone or frustum volume?

Accepted Answer

Cone volume = πr²h/3, where r is the base radius and h is the height. Frustum (truncated cone) volume = πh/3 × (R² + Rr + r²), where R is the base radius, r is the top radius. Slant height = √(h² + (R−r)²). Used for: conical roofs, spire caps, grain silos, tapered concrete piles, and hoppers.

Question 7

How do you calculate the area of a regular polygon pad?

Accepted Answer

Area = (n × s²) ÷ (4 × tan(π/n)), where n = number of sides and s = side length. For an octagon with 1.8 m sides: Area = (8 × 3.24) ÷ (4 × tan(22.5°)) = 25.92 ÷ 1.657 = 15.64 m². The miter cut for joining frame members = 180° ÷ n = 22.5° for an octagon. Used for gazebo pads, turret bases, and bay window footings.

Question 8

How do you calculate the area of an L-shaped room?

Accepted Answer

Divide the L-shape into two rectangles. Measure each rectangle's length and width separately, calculate Area = L×W for each, then add them together. For a 6 m × 4.5 m section plus a 3 m × 2.4 m section: Total = 27 + 7.2 = 34.2 m². If sections overlap at a corner, subtract the overlapping area to avoid double-counting.

Question 9

What is the end-area method for earthwork volume?

Accepted Answer

End-Area Method: Volume = ½ × (A₁ + A₂) × L, where A₁ and A₂ are the cross-sectional areas at each end and L is the distance between them. For A₁ = 20 m², A₂ = 15 m², L = 15 m: V = ½ × 35 × 15 = 262.5 m³. The more accurate Prismatoid formula adds a mid-section: V = L/6 × (A₁ + 4Aₘ + A₂). AASHTO recommends prismatoid for curved or irregular sections.

Question 10

How much does excavated soil swell?

Accepted Answer

Excavated (loose) volume is always larger than bank (in-place) volume due to swell. Typical swell factors: clay/till = 20–40%, sand/gravel = 10–15%, rock = 30–60%. Multiply bank volume by (1 + swell%) to get loose truck volume. OSHA 1926 Subpart P classifies soil types A, B, and C — each with different stability and swell characteristics.

Question 11

What is the minimum concrete slab thickness for a residential floor?

Accepted Answer

ACI 332-14 §5.5.1 specifies a minimum 4 inches (100 mm) for residential concrete slabs-on-grade. Commercial light-duty floors: 5–6 inches (125–150 mm) per ACI 360R-10. Industrial floors may require 6–8 inches or more depending on load. Always consult a structural engineer for specific load requirements.

Question 12

How many cubic yards of concrete are in a cubic meter?

Accepted Answer

1 cubic meter = 1.308 cubic yards. Conversely, 1 cubic yard = 0.7646 cubic meters = 27 cubic feet. To convert m³ to yd³: divide by 0.7646 (or multiply by 1.308). To convert ft³ to yd³: divide by 27. The calculator outputs both m³ and yd³ for all volume results to simplify concrete ordering.

面積/体積計算機: Complete Guide with Formulas and Real-World Applications

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