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 centimetres.

If 1 cubic centimetre of the metal weighs 6.6 g, calculate the weight of the piece of metal to the nearest kg.

(i) Area of cross-section = Area of rectangle ABCE + Area of Δ DEF

= length x breadth + $\dfrac{1}{2}$ x base x height

= 12 x 10 + $\dfrac{1}{2}$ x (16 - 10) x (12 - 7.5) m²

= 120 + $\dfrac{1}{2}$ x 6 x 4.5 m²

= 120 + 3 x 4.5 m²

= 120 + 13.5 m²

= 133.5 m²

Hence, the area of cross-section is 133.5 m².

(ii) Length of the piece of metal = 4 m = 400 cm

Volume of the piece of metal = Area of cross-section x length

= 133.5 x 400 cm³

= 53,400 cm³

Weight of 1 cubic cm of metal = 6.6 g

Weight of 53,400 cubic cm metal = 6.6 x 53,400 g

= $\dfrac{352,440}{1000}$ kg = 352.44 kg ≈ 352 kg.

Hence, the volume of the piece of metal is 53,400 cm³ and weight of the piece of metal is 352 kg.