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Question
The cross-section of a piece of metal 4 m in length is shown below. Calculate :
(i) The area of the cross-section;
(ii) The volume of the piece of metal in cubic centimeters.
If 1 cubic centimeter of the metal weighs 6.6 g, calculate the weight of the piece of metal to the nearest kg.
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Solution
(i) Area of total cross section = Area of rectangle abce + area of Δdef
= ( 12 x 10 ) + `1/2` ( 16 - 10 )( 12 - 7.5 )
= 120 + `1/2` (6)( 4.5 ) cm2
= 120 + 13.5 cm2
= 133.5 cm2
(ii) The volume of the piece of metal in cubic centimeters = Area of total cross section x length
= 133.5 cm2 x 400 cm2 = 53400 cm3
1 cubic centimetre of the metal weighs 6.6 g
53400 cm3 of the metal weighs 6.6 x 53400 g = `(6 .6 xx 53400)/(1000)` kg
= 352.440 kg
The weight of the piece of metal to the nearest Kg is 352 Kg.
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