Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 583 · 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 4 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 136 cu cm (d) 80 cu 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) 1386 sq cm (d) 132 sq cm
3. 3.A cuboid is 11 cm long, 9 cm wide and 7 cm high. What is its volume? (a) 693 cu cm (b) 478 cu cm (c) 99 cu cm (d) 27 cu cm
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
5. 5.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
6. 6.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) 4 times (c) 8 times (d) 2 times
7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
9. 9.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) 9 times (c) 6 times (d) 27 times
10. 10.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
11. 11.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 64 sq cm (d) 384 sq cm
12. 12.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) 5 times (c) 10 times (d) 25 times
13. 13.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
14. 14.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 24 cu cm (d) 256 cu cm
15. 15.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 24 cu cm (b) 17 cu cm (c) 168 cu cm (d) 188 cu cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
17. 17.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
18. 18.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
19. 19.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
20. 20.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
21. 21.A cuboid is 11 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 26 cu cm (b) 616 cu cm (c) 77 cu cm (d) 442 cu cm
22. 22.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 30 cu cm
23. 23.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
24. 24.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
25. 25.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
28. 28.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
29. 29.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 8 cu cm (b) 17 cu cm (c) 16 cu cm (d) 40 cu cm
30. 30.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) 64 times (c) 8 times (d) 16 times
31. 31.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
32. 32.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
33. 33.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 8 cu cm (d) 16 cu cm
34. 34.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
35. 35.A cuboid is 5 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 56 sq cm (b) 224 sq cm (c) 80 sq cm (d) 112 sq cm
36. 36.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
37. 37.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
38. 38.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 60 cu cm (c) 20 cu cm (d) 12 cu cm
39. 39.A cuboid is 10 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 190 cu cm (b) 150 cu cm (c) 18 cu cm (d) 50 cu cm
40. 40.A cuboid is 12 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 144 cu cm (b) 192 cu cm (c) 19 cu cm (d) 36 cu cm

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