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.

Answer 1

(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.