Calculating the Mass of Portland Cement Concrete
How many kilograms of Portland cement concrete (PCC) are required to cast a cylindrical column?
Portland cement concrete (PCC) has a density of 150 lb/ft³. How many kilograms of PCC are required to cast a cylindrical column 1.15 m in diameter and 7.8 m in height? (1 kg = 2.205 lb, 1 inch = 2.54 cm)
Choose the correct option:
a) 19466.7 kg
Answer
The correct answer is 19466.7 kg
To calculate the mass of Portland cement concrete required to cast a cylindrical column, we first need to understand the given data:
- Density of Portland cement concrete (PCC) = 150 lb/ft³
- Diameter of the cylinder = 1.15 m
- Height of the cylinder = 7.8 m
- 1 kg = 2.205 lb
Given the density of PCC in lb/ft³, we need to convert it to kg/m³:
1 lb/ft³ = 16.018 kg/m³
Therefore, 150 lb/ft³ = 2402.77 kg/m³
Using the formula for density [tex]d=\\dfrac{m}{V}[/tex], where m is the mass of PCC in kg and V is the volume of the cylinder, we can calculate the mass:
[tex]m=d\\times V[/tex]
[tex]m=d\\times \\pi r^2 h\\\\m=2402.77\\times \\pi \\times (1.15/2)^2\\times 7.8\\\\m=19466.70\\ kg[/tex]
Therefore, the mass of Portland cement concrete required to cast the cylindrical column is 19466.7 kg.