Question

a triangular slab has a base of 16 ft, a height of 12 ft, and is 5 inches thick.
how many cubic yards of concrete are required?
your answer

a barn entry slab is shaped like a trapezoid with bases of 22 ft and 30 ft, a height of 12 ft, and a thickness of 6 inches.
how many cubic yards of concrete are needed?
your answer

what is the chemical process that causes concrete to harden? *
a. oxidation
b. evaporation
c. hydration
d. fermentation

Explanation:

First Problem (Triangular Slab)

Step1: Convert thickness to feet

Since 1 foot = 12 inches, thickness $t = \frac{5}{12}$ ft

Step2: Calculate triangular base area

Area of triangle: $A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 16 \times 12 = 96$ sq ft

Step3: Calculate volume in cubic feet

Volume $V_{\text{ft}^3} = A \times t = 96 \times \frac{5}{12} = 40$ cubic ft

Step4: Convert to cubic yards

Since 1 cubic yard = 27 cubic feet, $V_{\text{yd}^3} = \frac{40}{27} \approx 1.48$

Step1: Convert thickness to feet

Thickness $t = \frac{6}{12} = 0.5$ ft

Step2: Calculate trapezoid base area

Area of trapezoid: $A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} = \frac{1}{2} \times (22+30) \times 12 = 312$ sq ft

Step3: Calculate volume in cubic feet

Volume $V_{\text{ft}^3} = A \times t = 312 \times 0.5 = 156$ cubic ft

Step4: Convert to cubic yards

$V_{\text{yd}^3} = \frac{156}{27} \approx 5.78$

Concrete hardens when cement particles react chemically with water, forming solid crystalline structures that bind the aggregate together. This process is called hydration, not oxidation, evaporation, or fermentation.

Answer:

$\frac{40}{27}$ or approximately 1.48 cubic yards

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Second Problem (Trapezoidal Slab)