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Shapes, volumes and perspective.
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Worked examples
Twenty questions from this topic with their answer and the method used. Start the quiz above to practise with other variants.
On a 1:100 scale plan, a segment is 7 cm long. Real length in metres?
Answer 7
7 × 100 cm = 7 m.
A circle has radius 38 cm. Its circumference is kπ cm. What is k?
Answer 76
P = 2πr = 76π cm; k = 76.
A cube has edge length 47 cm. Volume in cm³?
Answer 103,823
V = 47³ = 103823 cm³.
A cuboid measures 7 × 12 × 2 cm. Volume in cm³?
Answer 168
V = 7 × 12 × 2 = 168 cm³.
What is the interior angle sum of a convex 23-sided polygon, in degrees?
Answer 3,780
(23 − 2) × 180° = 3780°.
A triangle has base 12 cm and perpendicular height 11 cm. Area in cm²?
Answer 66
A = (12 × 11) ÷ 2 = 66 cm².
A rectangle is 3 cm by 18 cm. What is its area in cm²?
Answer 54
A = 3 × 18 = 54 cm².
What is the perimeter in cm of a 7 cm by 9 cm rectangle?
Answer 32
P = 2 × (7 + 9) = 32 cm.
On a 1:100 scale plan, a segment is 24 cm long. Real length in metres?
Answer 24
24 × 100 cm = 24 m.
A circle has radius 20 cm. Its circumference is kπ cm. What is k?
Answer 40
P = 2πr = 40π cm; k = 40.
A cube has edge length 14 cm. Volume in cm³?
Answer 2,744
V = 14³ = 2744 cm³.
A cuboid measures 6 × 16 × 2 cm. Volume in cm³?
Answer 192
V = 6 × 16 × 2 = 192 cm³.
What is the interior angle sum of a convex 9-sided polygon, in degrees?
Answer 1,260
(9 − 2) × 180° = 1260°.
A triangle has base 10 cm and perpendicular height 12 cm. Area in cm²?
Answer 60
A = (10 × 12) ÷ 2 = 60 cm².
A rectangle is 6 cm by 17 cm. What is its area in cm²?
Answer 102
A = 6 × 17 = 102 cm².
What is the perimeter in cm of a 4 cm by 16 cm rectangle?
Answer 40
P = 2 × (4 + 16) = 40 cm.
On a 1:100 scale plan, a segment is 13 cm long. Real length in metres?
Answer 13
13 × 100 cm = 13 m.
A circle has radius 31 cm. Its circumference is kπ cm. What is k?
Answer 62
P = 2πr = 62π cm; k = 62.
A cube has edge length 52 cm. Volume in cm³?
Answer 140,608
V = 52³ = 140608 cm³.
A cuboid measures 7 × 14 × 2 cm. Volume in cm³?
Answer 196
V = 7 × 14 × 2 = 196 cm³.