2.2 Space and shape  (Page 2/3)

TSA = 2 base area + sides area = (2 × s ² ) + (H × base perimeter)

s = 28mm

Step 1: Determine what the base is

and sketch it with its dimensions.

Step 2: Calculate the base area.

Base area = s ² = 28 ² = 784 mm ²

Step 3: Calculate the base perimeter.

Base perimeter = 4 × s = 112mm

Step 4: Write down the height of the prism.

H = 52mm

Step 5: Calculate the TSA and V.

V = 784 × 52 = 40 768 mm ³ ≈ 40,7 cm ³

TSA = (2 × 784) + (52 × 112) = 7 392 mm ² ≈ 73,9 cm ²

1. Rectangular prism :

TSA = 2 base area + sides area = 2 (l × b) + (H × base perimeter)

1 = 41mm; b = 14mm

Step 1: Determine what the base is and sketch it with its dimensions.

Step 2: Calculate the base area.

Base area = l × b = 41 × 14 = 574 mm ²

Step 3: Calculate the base perimeter.

Base perimeter = 2 (14 + 41) = 110mm

Step 4: Write down the height of the prism.

H = 54mm

Step 5: Calculate the TSA and V.

V = 574 × 54 = 30 996 mm ³ ≈ 31 cm ³

TSA = (2 × 574) + (54 × 110) = 7 088 mm ² ≈ 70,1 cm ²

1. Cylinder :

r = 17,5mm

Step 1: Determine what the base is and sketch it with its dimensions.

Step 2: Calculate the base area.

Base area = π r ² = 3,14159 × (17,5) ² ≈ 962,1mm ²

Step 3: Calculate the base perimeter.

Base perimeter = 2 π r = 109,956mm

Step 4: Write down the height of the prism.

H = 60,5mm

Step 5: Calculate the TSA and V.

V = 962,1 × 60,5 ≈ 58 207,8 mm ³ ≈ 58 cm ³

TSA = (2 × 962,1) + (60.5 × 109,956) ≈ 8 576,55 mm ² ≈ 85,8 cm ²

1. Triangular prism :

TSA = 2 base area + sides area = 2 (½ × b × h) + (H × base perimeter)

b = 43,5mm; h = 31,5mm

hypotenuse = 53,7mm (Pyth.)

Step 1: Determine what the base is and sketch it with its dimensions.

Step 2: Calculate the base area.

Base area = ½ b × h = 685,125 ≈ 685,1mm ²

Step 3: Calculate the base perimeter.

Base perimeter = b + h + hypotenuse ≈ 128,7mm

Step 4: Write down the height of the prism.

H = 60,5mm

Step 5: Calculate the TSA and V.

V = 685,1 × 60,5 ≈ 41 450,1 mm ³ ≈ 41 cm ³

TSA = (2 × 685,1) + (60.5 × 128,7) ≈ 9 157,06 mm ² ≈ 91,6 cm ²

Exercise:

Calculate the total surface area and the volume of each of the following three prisms.

Assignment to be done in pairs:

• Help Granny solve her problem. She has cooked a pot of peach jam. The jam is 2 cm from the top rim of her cooking pot which has a diameter of 24 cm and is 21 cm high.
• She has some pretty jam jars which she wants to fill to about ½ cm from the top.
• She has two types of jam jar. The brown kind has a square base (8 cm × 8 cm) and is 12 cm high, and the yellow kind has a base of 6,5 cm × 11,5 cm and is 11 cm high. There are eleven of each kind.
• Her problem is that she wants to use only one type of jar for the peach jam. This means that she does not want to start filling one kind of jar and then find that she has jam left over when she has used up all eleven jars.
• Your job is to find out for her whether she has enough jars of one type to fit her jam into, and to tell her which kind to use.

Activity 2

To become acquired with various two- and three-dimensional figures

[LO 3.1, 3.5]

A. Two-dimension a l figures

These are figures that can be drawn on flat paper. Therefore they are called pl a ne figures. Of course there are limitlessly many such figures.