Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 790 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
2. 2.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
5. 5.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 4 sq cm (c) 8 sq cm (d) 16 sq cm
6. 6.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
7. 7.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
8. 8.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
9. 9.A cuboid is 8 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 112 sq cm (b) 64 sq cm (c) 224 sq cm (d) 56 sq cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
12. 12.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
13. 13.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 64 cu cm (d) 12 cu cm
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
15. 15.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
16. 16.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
17. 17.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 256 sq cm (c) 512 sq cm (d) 64 sq cm
18. 18.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
19. 19.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
20. 20.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 64 cu cm (b) 8 cu cm (c) 10 cu cm (d) 32 cu cm
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
22. 22.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
23. 23.A cuboid is 7 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 21 cu cm (b) 13 cu cm (c) 63 cu cm (d) 102 cu cm
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
25. 25.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
26. 26.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
27. 27.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
28. 28.A cuboid is 9 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 18 cu cm (b) 20 cu cm (c) 162 cu cm (d) 234 cu cm
29. 29.A cuboid is 6 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 14 cu cm (b) 128 cu cm (c) 24 cu cm (d) 96 cu cm
30. 30.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
31. 31.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
33. 33.A cuboid is 9 cm long, 8 cm wide and 4 cm high. What is its volume? (a) 72 cu cm (b) 280 cu cm (c) 288 cu cm (d) 21 cu cm
34. 34.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 148 sq cm (b) 120 sq cm (c) 296 sq cm (d) 74 sq cm
35. 35.A cuboid is 9 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 588 sq cm (b) 294 sq cm (c) 147 sq cm (d) 270 sq cm
36. 36.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
37. 37.A cuboid is 9 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 450 cu cm (b) 370 cu cm (c) 24 cu cm (d) 45 cu cm
38. 38.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
39. 39.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
40. 40.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times

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