Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 763 · 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 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 24 sq cm (d) 8 sq cm
2. 2.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
4. 4.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
6. 6.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
7. 7.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
8. 8.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
9. 9.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
10. 10.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
11. 11.A cuboid is 7 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 70 cu cm (b) 35 cu cm (c) 118 cu cm (d) 14 cu cm
12. 12.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 24 cu cm (b) 52 cu cm (c) 9 cu cm (d) 6 cu cm
13. 13.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 400 cu cm (c) 30 cu cm (d) 600 cu cm
14. 14.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) 4 times (c) 16 times (d) 64 times
15. 15.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 125 cu cm (d) 100 cu cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
17. 17.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) 16 times (d) 8 times
18. 18.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 18 cu cm (b) 42 cu cm (c) 8 cu cm (d) 6 cu cm
19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
20. 20.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 54 cu cm (d) 36 cu cm
21. 21.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
22. 22.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) 8 times (c) 6 times (d) 4 times
23. 23.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 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) 4 times (b) 8 times (c) 5 times (d) 2 times
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
26. 26.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 64 sq cm (c) 384 sq cm (d) 512 sq cm
27. 27.A cuboid is 10 cm long, 9 cm wide and 3 cm high. What is its total surface area? (a) 270 sq cm (b) 147 sq cm (c) 588 sq cm (d) 294 sq cm
28. 28.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
29. 29.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
30. 30.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
31. 31.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 726 sq cm
32. 32.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 50 sq cm (b) 56 sq cm (c) 200 sq cm (d) 100 sq cm
33. 33.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 21 cu cm (d) 343 cu cm
34. 34.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
36. 36.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 60 sq cm (b) 208 sq cm (c) 52 sq cm (d) 104 sq cm
37. 37.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 60 cu cm (b) 104 cu cm (c) 13 cu cm (d) 30 cu cm
38. 38.A cuboid is 9 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 576 sq cm (b) 416 sq cm (c) 832 sq cm (d) 208 sq cm
39. 39.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 15 cu cm (b) 112 cu cm (c) 6 cu cm (d) 60 cu cm
40. 40.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 24 cu cm (d) 512 cu cm

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