my questions is where does the 3, 5 and 12 come from in the question below what
ID: 3281127 • Letter: M
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my questions is where does the 3, 5 and 12 come from in the question below what shape/geometry is used?
it is highlighted with a question mark? the geometry of the problem and how the values are found and the shapes used is my question.
Problem 5.64 The aluminum s density of aluminum is 2800 kg/m', determine the mass of the shade. imum shade for the small high-intensity lamp shown has a uniform thickness of I mm. Knowingt 66mm 56 min 32 mm 26 mm. , 8 mm 2 3 2+23133121-5 2 32 13 © McGraw-Hill Education This is proprietary matenal solely for authorized instructor use. Not Copyright orized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, whole or part forwarded, distributed, or posted on a website, in bahaa Ansaf: CSU-puebloExplanation / Answer
the mass of the shade can be found by multiplying the tyotal surface area with the thickness to find the volume and then from the density the mass can be found
now, total sirface area of the shade = area of circular part (A1) + curved surface area of the trapezium in the top part (A2) + curved surface area of the trapezium in the middle part (A3) + curved surface area of the trapezium in the top part (A4)
now A1 = pi*26^2/4 = 530.929 mm^2
A2 = pi*32*(32 + 26) = 5830.795 mm^2
A3 = pi*8(56 + 32) = 2211.68 mm^2
A4 = pi*28(66 + 56) = 10731.68 mm^2
total surface area = A = A1 + A2 + A3 + A4 = 19305.084 mm ^2 = 0.019305084 m^2
density, rho = 2800 kg/m^3
thickness, t = 1mm = 0.001 m
volume = At
mass = rho*A*t = 0.0540542352 kg = 54.0542352 g
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