Question 1 of 3Measures & Mensuration
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A car tank holds 22 1/2 litres of fuel when it is 3/8 full. Calculate the amount of fuel when it is full.
The diagram shows a trough in the form of a prism whose cross section ABCD is a trapezium with AD parallel to BC and the measurements are in centimetres. AD = 40, BC = 21, AB = 18, the perpendicular height from BC to AD is 14 and the trough is 90 long. (a)(i) Calculate the area of the cross-section ABCD of the trough. (ii) Calculate the capacity of the trough when full. (b) The inside of the trough is to be painted. One litre of the paint covers an area of 1 496 cm^2. (i) Calculate the area of the trough to be painted. (ii) Calculate the number of litres of paint needed to paint the inside of the trough to the nearest litre. (iii) Calculate the cost of the paint if one litre of the paint costs $6,30.
The diagram shows the cross-section of a garden shed. The cross-section ABCDE is made up of a rectangle measuring 2 m by 2,2 m and an isosceles triangle with a perpendicular height of 0,6 m and a base of 2 m. (a) Calculate the area of the cross-section. (b) If the shed is 3 m long, calculate the volume of the shed. (c) It is given that 23 m^2 of the surface area of the shed need to be painted and that one tin of paint covers an area of 4,5 m^2. Calculate the number of tins of paint that have to be bought to cover the 23 m^2. (d)(i) Calculate the length of the edge DE. (ii) The sloping roof is to be covered by roofing material which costs $6.40 per square metre. Calculate the cost of roofing material needed to cover the sloping roof.
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