4024/22 May/Jun 2022, Question 4: Pythagoras' Theorem

Part (ai) · 2 marks

Work out the area of the pentagon from the diagram, giving the result in cm².

1. 1Split into a 4 × 15 rectangle and a triangle
2. 2Rectangle = 4 × 15 = 60
3. 3Triangle: base 12 − 4 = 8, height 15 − 9 = 6, area = 1/2 × 8 × 6 = 24
4. 4Area = 60 + 24 = 84 cm²

Answer84

Part (aii) · 3 marks

Work out the total distance around the pentagon, in centimetres.

1. 1Sloping side = √(8² + 6²)
2. 2= √100 = 10
3. 3Perimeter = 12 + 15 + 4 + 9 + 10 = 50 cm

Answer50

Part (b) · 3 marks

Use the sphere volume formula to determine the radius of a sphere whose volume is 2572 cm³.

1. 14/3 πr³ = 2572
2. 2r³ = (2572 × 3)/(4π) = 614.0…
3. 3r = ∛614.0… = 8.498…
4. 4r = 8.50 cm

Answer8.5 or 8.49 to 8.50

Part (ci) · 3 marks

Work out the total surface area of the 2 cm by 6 cm by 22.5 cm cuboid.

1. 1Face areas: 2 × 6 = 12, 2 × 22.5 = 45, 6 × 22.5 = 135
2. 2Surface area = 2 × (12 + 45 + 135)
3. 3= 2 × 192 = 384 cm²

Answer384

Part (cii) · 3 marks

For a cube of edge x cm with the same surface area as the cuboid, write an equation in x and solve it, showing your working.

1. 1A cube has 6 square faces: 6x² = 384
2. 2x² = 64
3. 3x = 8 cm

Answer8

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