Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 138 · 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 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 16 sq cm (d) 96 sq cm
2. 2.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
3. 3.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) 125 times (c) 5 times (d) 25 times
4. 4.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 66 cu cm (b) 10 cu cm (c) 12 cu cm (d) 36 cu cm
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
7. 7.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 196 cu cm (d) 294 cu cm
8. 8.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 400 cu cm
9. 9.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
10. 10.A cuboid is 8 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 128 sq cm (b) 96 sq cm (c) 192 sq cm (d) 384 sq cm
11. 11.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 216 sq cm (d) 217 sq 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) 10 times (b) 5 times (c) 125 times (d) 25 times
13. 13.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
16. 16.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 82 cu cm (b) 42 cu cm (c) 12 cu cm (d) 14 cu cm
17. 17.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) 5 times (c) 25 times (d) 10 times
18. 18.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
19. 19.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
20. 20.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 61 sq cm (b) 244 sq cm (c) 84 sq cm (d) 122 sq cm
21. 21.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
22. 22.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
23. 23.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 9 sq cm (d) 27 sq cm
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
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.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 512 cu cm (d) 384 cu cm
27. 27.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 125 cu cm (d) 100 cu cm
28. 28.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 95 sq cm (b) 380 sq cm (c) 126 sq cm (d) 190 sq cm
29. 29.A cuboid is 12 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 24 cu cm (b) 19 cu cm (c) 120 cu cm (d) 188 cu cm
30. 30.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) 9 times (c) 3 times (d) 27 times
31. 31.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 486 sq cm (d) 81 sq cm
32. 32.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
33. 33.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 144 sq cm
34. 34.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
35. 35.A cuboid is 10 cm long, 8 cm wide and 2 cm high. What is its volume? (a) 232 cu cm (b) 20 cu cm (c) 160 cu cm (d) 80 cu cm
36. 36.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 248 cu cm (b) 24 cu cm (c) 240 cu cm (d) 20 cu cm
37. 37.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
38. 38.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
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
40. 40.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm

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