mathematical literacy learner notes
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NORTHERN CAPE DEPARTMENT OF EDUCATION
MATHEMATICAL
LITERACY
LEARNER NOTES
PERIMETER, AREA AND
SURFACE AREA
2
PERIMETER, AREA AND SURFACE AREA
Check that all measurements are in the same units, otherwise first convert all units into
those specified by the question, before doing calculations.
PERIMETER
The border or outer boundary lengths of a two-dimensional figure.
The perimeter of a circle is known as a circumference.
Since perimeter has to do with lengths, the units of perimeter are mm, cm, m or km.
3
AREA
The surface enclosed by the boundary lengths of a two-dimensional figure.
Since area is the product of two-dimensional lengths, the units of area are mm², cm², m²
or km².
TOTAL SURFACE AREA
The total exterior area of all the exposed surfaces of a three dimensional object.
The only difference between total surface area (TSA) and area, is that TSA refers to 3-D
objects, while area refers to 2-D objects.
Since TSA is the sum of all the areas, the units of TSA are mm², cm², m², or km².
Rectangular prism = (2 × length × breadth) + (2 × length × height) + (2 × breadth × height)
Cylinder = [2 × π × (radius)²] + [2 × π × (radius) × height] where π = 3,142
4
QUESTION 1
Jolandi decides to make place mats from wooden planks for each guest at her wedding
reception. She has 125 guests (including the bride and groom). The place mats are
rectangular, as indicated in the diagram below.
Each place mat consists of 2 vertical wooden planks onto which 6 horizontal planks are
attached. Each plank is 30 mm wide and 5 mm thick.
PHOTO OF PLACE MAT
DIAGRAM OF PLACE MAT
[Adapted from: www.pinterest.com]
Use the information above and answer the questions that follow.
1.1 Calculate the total area that will be covered by one place mat.
You may use the following formula:
Area of rectangle = length × width
(2)
1.2 To make one place mat, each plank is varnished individually on the front and
back before it is attached.
Varnish are sold in 1 litre cans. An area of 12 m² can be covered by one can of
varnish.
Calculate how many cans of varnish Jolandi will need to varnish all the place
mats for all the guests.
(7)
30,5 cm
23 cm
30 mm
5
QUESTION 2
2.1 Liam and Amy are planning their wedding. Amy wants a four-layer red velvet
wedding cake. She must still decide between a cylindrical or rectangular cake as
shown on ANNEXURE A.
Use ANNEXURE A to answer the questions that follow.
2.1.1 Determine the total height of the cylindrical cake in millimetres. (3)
2.1.2 The base (bottom) layer of the cylindrical cake has a radius of 14
cm.
Determine the diameter of the base layer in cm.
(2)
2.1.3 Define the term perimeter. (2)
2.1.4 Calculate the area (in cm2) of the base of the pan needed to bake the
top layer of the rectangular cake.
You may use the following formula:
Area = length × width
(2)
2.2 Aunt Abby will bake the wedding cake. She will be using a recipe from a recipe
book published in England.
NOTE:
1 kg = 2,25 pounds
1 mℓ flour = 0,7 g flour
2.2.1 Aunt Abby needs 3 and a half pounds of butter.
Determine the mass of butter, in kilogram.
(2)
2.2.2 Aunt Abby only has a kitchen scale available.
If aunt Abby needs 625 mℓ of flour, determine the mass of the flour
in grams.
(2)
2.2.3 The cake must be baked at 356 °F.
Determine to what degree Celsius the oven should be turned.
You may use the following formula:
°C = (°F – 32°) ÷ 1,8
(2)
[15]
6
ANNEXURE A
QUESTION 2.1
FOUR-LAYER RED VELVET WEDDING CAKES
AMY'S FOUR-LAYER CYLINDRICAL RED VELVET WEDDING CAKE
height = h
AMY'S FOUR-LAYER RECTANGULAR RED VELVET WEDDING CAKE
35 cm
Length of top layer = 15 cm
Length of bottom layer = 35 cm
Width of top layer = 12 cm
Width of bottom layer = 33 cm
[Adapted from www.pinterest.com]
15 cm
Top layer
Base
(bottom)
layer
33 cm
12 cm
7
QUESTION 3
Petru makes craft products that she sells at a craft market. She makes gift stockings (gift bags
shaped like a sock) decorated with triangular shapes, as shown below. She sews three
triangles onto each side of the stocking.
Photograph of a gift
stocking
Dimensions of the
triangular pieces of
fabric
Dimensions of a
rectangular piece of
fabric required for one
side of a stocking
[www.marthastewart.com]
3.1 The area of one side of a stocking (without the triangular pieces) is 355,25 cm².
Calculate the area of the fabric that is left over if Petru cuts ONE complete
stocking from two rectangular pieces of fabric.
You may use the following formula:
Area of rectangle = length × width
(6)
3.2 Calculate the total area of the triangular shapes needed to decorate ONE
stocking.
You may use the following formula:
Area of triangle = 2
1× base × height
(4)
3.3 It takes Petru 18 minutes to cut, decorate and hand-stitch one stocking.
Determine at what time she will finish making NINE stockings if she starts at
08:25.
(4)
[14]
5 cm
3 cm
8
QUESTION 4
Below is a photograph of a glass ornament that Petru makes using 250 mℓ cylindrical glass
jars.
The inside radius of the glass jar is 3,25 cm.
The outside diameter of the lid of the jar is 72 mm and the height (h) is 9 mm.
The exterior surface of the lid is painted red.
The jar is filled 75% with water and a pinch of glitter is added to the water. A dash of
glycerine is also added to keep the glitter from sinking too quickly.
The figure is glued to the inside of the lid before the lid is placed on the jar. The jar is then
turned upside down.
4.1 Calculate (to the nearest cm²) the exterior surface area of the lid that needs to be
painted.
You may use the following formula:
Painted exterior surface area of lid = 2h) (r πr where 𝝅 = 3,142; r is the radius and h is the height of the lid.
(4)
4.2 Use the conversions below to answer the following questions.
1 pinch = 16
1
teaspoon
2 pinches = 1 dash
1 teaspoon = 5 mℓ
Determine what fraction of a teaspoon equals ONE dash.
(2)
[06]
9
QUESTION 5
5.1 Justin has an injury that requires him to use a wheelchair for a while. He uses the
diagrams below to determine certain dimensions of the wheelchair.
Side view of the wheelchair Front view of the wheelchair
[Source: 1800wheelchair.com]
Use the diagrams above to answer the following questions.
5.1.1 The outer diameter of the bigger wheel is 54% of the length of the
wheelchair.
Determine the length of the outer diameter (rounded off to the
nearest mm) of the big wheel.
(4)
5.1.2 The big wheel has 24 equally
spaced cylindrical spokes
attached to the rim, as shown
in the picture alongside.
The diameter of each spoke
is 2 mm.
The inner diameter of the rim
is 584 mm.
Calculate how far apart the wheel spokes are spaced from each other on
the rim.
You may use the following formula:
Circumference of a circle = π × diameter using π = 3,142
(6)
5.1.3 One of the doorway openings in Justin's house is 750 mm wide.
Determine, showing ALL calculations, how wide (in mm) the available
gap on both sides of the wheelchair is if the wheelchair passes through the
doorway opening exactly in the middle.
(4)
Width
Length
Big wheel
121,92 cm 60,96 cm
10
5.2 The doorway of a museum is shown in the photograph and diagram below. It has two
identical doors that can open to allow for the easy flow of people.
The doors have glass-panel inserts, in the shape of rectangles and quarter circles,
embedded in a wooden frame, as shown in the photograph and diagram below.
The following formulae may be used:
Area of a rectangle = length × width
Area of a circle = π × (radius)2 using π = 3,142
Use the diagram above to answer the following questions.
5.2.1 Determine the total width, in metres, of the two doors. (3)
5.2.2 Calculate the value of e, the length of the rectangular glass-panel inserts. (4)
5.2.3 Calculate the total area (in mm2) of ALL the glass-panel inserts. (6)
[27]
11
QUESTION 6
6.1 Confidence was interested in the amount of hours that she spend sleeping and the quality of
sleep. She tracked her sleeping pattern for seven (7) days using the fitness monitor watch.
TABLE 4: SLEEPING PATTERN TIMES IN HOURS AND MINUTES
Day Total Sleep Restful Sleep % Restless Sleep %
Monday 5h28min K 86 0h45min 14
Tuesday 7h16min 6h27min 89 0h49min 11
Wednesday 6h57min 5h57min 86 1h0min 15
Thursday 5h45min 5h33min 97 1h12min 3
Friday 7h11min 5h41min 79 1h30min 21
Saturday 8h39min 6h35min 76 2h04min 24
Sunday 8h35min 6h17min 73 2h18min 27
[Source: www.androidcentral.com]
NOTE: The minimum recommended total sleeping time for an adult is 7 hours per day.
6.1.1 Write down the restless sleeping time (in minutes) for Saturday. (2)
6.1.2 Name the day(s) on which Confidence exceeded the minimum recommended
sleeping time by LESS than 20 minutes.
(2)
6.1.3 Convert the time 6 hours 27 min to hours. (3)
6.1.4 Calculate K, the restful sleeping time (in hours and minutes) for Monday. (3)
6.1.5 Express the total sleeping time for Wednesday as a decimal of a day. (3)
6.1.6 Show that the total sleeping time from Monday to Sunday was 49h 51min. (3)
6.2 During the Idols South Africa music competition performances, contestants are allowed to
use the cylindrical stage as shown on ANNEXURE B. The diameter of the stage is
5 m and the height is 1,2 m.
6.2.1 Determine the radius of the stage. (2)
6.2.2 Calculate the area (to the nearest m²) of the stage. (3)
6.2.3 The manager wants to paint the sides of the stage with a special paint.
(a) Calculate the surface area of the sides of the stage. (2)
(b) The paint is sold in 1ℓ cans. Determine the number of 1ℓ cans of paint
that must be bought if a litre of paint covers an area of
2,4 m2.
(3)
[26]
12
ANNEXURE B
QUESTION 6.2
Idols South Africa music competition cylindrical stage.
The following formulae may be used:
Area circle = 𝝅 × r2
Lateral Surface Area of right circular cylinder = 𝟐 × 𝛑 × 𝐫 × 𝐡
NOTE: r = radius h = height and 𝛑 = 3,142
5 m
1,2 m
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