SAEP Matric Success – Zisukhanyo Maths Lit Worksheet

Tuesday 3rd March 2009

Estimating and measuring

1. The drawing below is the plan of a large washbasin. The parallel sides ABCD and EFGH are identical trapeziums. The other faces are all rectangles. The inside dimensions of the washbasin are:

Length AH = DE = 120 cmDepth AB = HG = 40 cmWidth at the bottom = BC = GF = 45 cmWidth at the top = AD = HE = 60 cm

a) Calculate the area of the trapezium ABCDb) Calculate the volume of the washbasin (in cm3)c) Express the capacity of the washbasin in litresd) If the washbasin is made of stainless steel, calculate the total area (in m2) of the stainless steel forming the basin

2. The drawing below shows the inside dimensions of a rondavel with a conical roof and no ceiling.a) Calculate the total volume of space under the roof in m3

b) Estimate the area of the wall by using π = 22/7 and subtracting 12m2 for the door and windowsc) Calculate the amount of paint required to paint the inside surface of the wall if 1 litre of paint covers 3,5 m2 of walld) Calculate the area of the conical roof and estimate the cost to thatch the roof if it costs R12,50 per m2 to do soe) Calculate the area of the floor of the rondavel and estimate the number of tiles needed to cover the floor if 25 tiles covers 1m2

3. Six tennis balls are packed into a cylindrical container with an inside diameter of 65 mm. The diameter of a tennis ball is 64 mm.a) What must be the inside height of the container be if allowance is made for 2 mm of extra height?b) Calculate the volume (in cm3) of:

i) the inside of the containerii) one tennis balliii) the space inside the container that is not taken up by the 6 tennis balls

c) Suppose the curved wall of the container is made of cardboard that is 1 mm thick. Calculate the area (in cm2) of the outside of the curved surface of the container if its outside height is 400 mm.

4. An entrepreneur that makes and sells buttons wants to make 1 200 buttons of the design below. It is a hemispherical top (radius 10 mm) with a cylindrical stem (diameter 6 mm and height 10 mm). The buttons are moulded from a plastic material after which a small hole is drilled through the stem. Calculate:a) the volume of one button in mm3 (ignore the small hole)b) the volume of plastic material required to mould 1 200 buttons in cm3 (add 10% to provide for wastage)c) the area of the hemispherical surface of one button in cm3

d) the amount of spray paint required to paint the hemispherical surfaces of 1 200 buttons if 1 ml of paint covers 25 cm2

5. The conical tent and hemispherical tent shown below have the same diameter (4 m) and maximum height (2 m). The base of each one is covered with a ground sheet. Calculate:a) the slant height of the conical tentb) the total surface area of each tentc) the volume of the space inside each tent (in litres)d) the ratio V half sphere : V cone

6. A silo for holding wheat in a flour mill is shaped as shown below. From the cylindrical top section the wheat moves down into a conical section where there is an outlet valve at QR. The small cone PQR has been “cut off” to provide an opening at QR. All the dimensions shown are inside dimensions. Calculate:a) the volume of the small cone PQR in m3

b) the capacity of the silo in m3

7. Write down the approximate conversions to the units below:a) 80 mph = … km/h b) 2,5 inches = … mmc) 1,5 yards = …ft and … inches d) 3 pints = … litrese) 10 lb = … kg

8. The lengths of three sides of a triangular plot of land are indicated on an old map as 600 yd, 700 yd and 900 yd.a) Convert the three lengths to metres if 1 yard = 0,91 m. Then calculate the perimeter of the plot in metres.b) Calculate the area of the plot in m2 using Heron’s formula.c) Express the area of the plot in ha (hectare).