Answer:
- area: 0.05498 m²
- volume: 0.10996 m³
- cost: $14.84
- weight: 267 kg
Explanation:
You want the volume, cost, and weight of a concrete pipe 2 m long with an outside diameter of 40 cm, and an inside diameter of 30 cm. The cost is $135 per cubic meter, and the weight is 2430 kg per cubic meter.
a. End area
The area of a circle in terms of its diameter is ...
A = π/4·d²
The area of the end of the pipe will be the difference between the overall area (using the outside diameter) and the area of the missing center part (using the inside diameter). It is ...
End area = (π/4)(0.40 m)² -(π/4)(0.30 m)² = 7π/400 m² ≈ 0.05498 m²
The area of the end of the pipe is about 0.05498 m².
b. Volume
The volume of the pipe is the product of its base area and its length:
V = Bh
V = (0.05498 m²)(2 m) ≈ 0.10996 m³
The volume of the pipe is about 0.10996 m³.
c. Cost
At $135 per cubic meter, the cost of the concrete for the pipe is ...
($135/m³)(0.10996 m³) ≈ $14.84
The concrete cost for the pipe is about $14.84.
d. Weight
The density of 2.43 g/cm³ is equivalent to 2430 kg/m³. Since our volume is in cubic meters, we need the density to have these units.
m = (2430 kg/m³)(0.10996 m³) ≈ 267.19 kg
The weight of the pipe is about 267 kg.
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Additional comment
The cost is given in units of dollars per cubic meter. This suggests that it will be convenient to use meters as the unit of length. The calculations are done with 30 cm and 40 cm converted to 0.30 m and 0.40 m, respectively.
Similarly, the density is converted to units of kg per cubic meter. This facilitates finding the weight in kg from the volume in m³.
1 g/cm³ = (0.001 kg)/(0.01 m)³ = 1000 kg/m³
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