Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 764 · 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 cuboid is 9 cm long, 7 cm wide and 9 cm high. What is its volume? (a) 567 cu cm (b) 63 cu cm (c) 414 cu cm (d) 25 cu cm
2. 2.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
7. 7.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) 16 times (c) 64 times (d) 8 times
8. 8.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 15 cu cm (d) 125 cu cm
9. 9.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 224 sq cm (c) 112 sq cm (d) 60 sq cm
10. 10.A cuboid is 8 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 192 cu cm (b) 16 cu cm (c) 18 cu cm (d) 128 cu 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) 176 cm (d) 2464 cm
12. 12.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) 5 times (c) 10 times (d) 125 times
13. 13.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 1331 cu cm (d) 726 cu cm
14. 14.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
15. 15.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
17. 17.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
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) 9856 sq cm (d) 176 sq cm
19. 19.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
20. 20.A cuboid is 8 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 528 sq cm (b) 264 sq cm (c) 288 sq cm (d) 132 sq cm
21. 21.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 729 sq cm (c) 81 sq cm (d) 324 sq cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
23. 23.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
24. 24.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 21 cu cm (c) 294 cu cm (d) 196 cu cm
25. 25.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
26. 26.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
27. 27.A cuboid is 6 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 126 cu cm (b) 18 cu cm (c) 14 cu cm (d) 90 cu cm
28. 28.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 222 sq cm (b) 111 sq cm (c) 189 sq cm (d) 444 sq cm
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 4 times (d) 8 times
31. 31.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) 27 times (c) 6 times (d) 3 times
32. 32.A cuboid is 9 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 288 sq cm (b) 140 sq cm (c) 280 sq cm (d) 560 sq cm
33. 33.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 729 cu cm (d) 324 cu cm
34. 34.A cuboid is 8 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 264 sq cm (b) 132 sq cm (c) 80 sq cm (d) 66 sq cm
35. 35.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
36. 36.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 25 sq cm (d) 125 sq cm
37. 37.A cuboid is 9 cm long, 8 cm wide and 4 cm high. What is its volume? (a) 21 cu cm (b) 280 cu cm (c) 72 cu cm (d) 288 cu cm
38. 38.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 400 cu cm
39. 39.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
40. 40.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 24 sq cm (d) 8 sq cm

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