Answer:
(b) 351.9 cm³
(c) 2287 g
(d) 13305 g ≈ 13.3 kg
Step-by-step explanation:
You want the volume and/or weight of pipes of various diameter, thickness, and density.
The volume of material in a pipe can be found as ...
V = π·(centerline diameter)(thickness)(length)
where the centerline diameter is the sum of the inside diameter (ID) and the wall thickness. The units of these dimensions need to be compatible, so some unit conversion may be necessary.
The weight of the pipe will be the product of its volume and the density of the material.
All of the given dimensions are in centimeters. The 2.6 cm internal radius corresponds to an inner diameter of 5.2 cm. The difference between the OD and the ID is (3 -2.6) = 0.4 cm.
The volume is ...
V = π(5.6 cm)(0.4 cm)(50 cm) = 112π cm³ ≈ 351.9 cm³
The density is given in terms of mm³, so we want to convert the dimensions to mm. The length is 1.4 m = 1400 mm.
The volume is ...
V = π(26 mm)(1 mm)(1400 mm) = 36400π mm³
The weight is ...
m = (0.02 g/mm³)(36400π mm³) = 728π g ≈ 2287 g
The density is given in terms of cm³, so we want to use cm for the dimensions. The 2 m length is 200 cm. The 5 mm thickness is 0.5 cm.
V = π(5.5 cm)(0.5 cm)(200 cm) = 550π cm³
The weight is ...
m = (7.7 g/cm³)(550π cm³) = 4235π g ≈ 13305 g ≈ 13.3 kg
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Additional comment
All of the problem numbers are given to 2 significant figures. However we don't feel quite right reporting the answers to 2 significant figures (350 cm³, 2.3 kg, 13 kg). Instead, we have generally used 3 or 4 significant figures.
