4024/21 May/Jun 2022, Question 4: Volume of a Prism

Part (a) · 2 marks

Given a cuboid measuring x cm by x cm by 10 cm with volume 62.5 cm³, determine x.

1. 1x × x × 10 = 62.5
2. 2x² = 6.25
3. 3x = 2.5

Answer2.5 or 2 1/2

Part (bi) · 1 mark

For a sector with radius 15 cm and angle 84°, demonstrate that its arc measures 7π cm.

1. 1Arc length = 84/360 × 2 × π × 15
2. 2= 84/360 × 30π
3. 3= 7π cm

Answer(84/360) × π × 2 × 15 leading to 7π or (84/180) × π × 15 leading to 7π

Part (bii) · 2 marks

The sector's two straight edges are brought together to make a cone; work out the cone's radius.

1. 1Arc length becomes the circumference of the base
2. 22 × π × r = 7π
3. 3r = 3.5 cm

Answer3.5 or 3 1/2

Part (biii) · 2 marks

Using the cone formed from the sector, determine its height.

1. 1Slant height = 15 cm
2. 2h² = 15² − 3.5² = 225 − 12.25 = 212.75
3. 3h = √212.75 = 14.58… ≈ 14.6 cm

Answer14.6 or 14.58 to 14.59

Part (c) · 3 marks

A cylindrical barrel of radius 20 cm and height 80 cm receives water at 5500 cm³ per minute; find the filling time in minutes and seconds to the nearest second.

1. 1Volume = π × 20² × 80 = 32 000π = 100 530.9… cm³
2. 2Time = 100 530.9… ÷ 5500 = 18.278… minutes
3. 30.278… × 60 = 16.7 seconds
4. 4Time = 18 minutes 17 seconds

Answer18 minutes 17 seconds

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