Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 942 · 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.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 150 sq cm (d) 125 sq cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
3. 3.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 256 cu cm (d) 512 cu cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
6. 6.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
8. 8.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 400 cu cm (d) 30 cu cm
9. 9.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
15. 15.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 6 cu cm (b) 32 cu cm (c) 12 cu cm (d) 7 cu cm
16. 16.A cuboid is 8 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 360 sq cm (b) 90 sq cm (c) 180 sq cm (d) 144 sq cm
17. 17.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
19. 19.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
20. 20.A cuboid is 6 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 252 sq cm (b) 90 sq cm (c) 126 sq cm (d) 63 sq cm
21. 21.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 9 cu cm (c) 54 cu cm (d) 36 cu cm
22. 22.A cuboid is 6 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 72 cu cm (b) 14 cu cm (c) 120 cu cm (d) 12 cu cm
23. 23.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
25. 25.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 729 cu cm (d) 324 cu cm
26. 26.A cuboid is 7 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 162 cu cm (b) 21 cu cm (c) 16 cu cm (d) 126 cu cm
27. 27.A cuboid is 12 cm long, 11 cm wide and 4 cm high. What is its total surface area? (a) 448 sq cm (b) 224 sq cm (c) 528 sq cm (d) 896 sq cm
28. 28.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 36 cu cm (d) 1728 cu cm
29. 29.A cuboid is 10 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 30 cu cm (b) 180 cu cm (c) 216 cu cm (d) 19 cu cm
30. 30.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
31. 31.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
32. 32.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
33. 33.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 16 sq cm (d) 97 sq cm
34. 34.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 8 times (d) 6 times
35. 35.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
36. 36.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 54 sq cm (b) 204 sq cm (c) 51 sq cm (d) 102 sq cm
37. 37.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
38. 38.A cuboid is 12 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 160 cu cm (b) 48 cu cm (c) 18 cu cm (d) 96 cu cm
39. 39.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
40. 40.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm

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