Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 120 · 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 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 384 cu cm (d) 512 cu cm
2. 2.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
3. 3.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
4. 4.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
5. 5.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
6. 6.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
7. 7.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 343 sq cm (d) 49 sq cm
8. 8.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
10. 10.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
11. 11.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 64 cu cm (d) 96 cu cm
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
13. 13.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
14. 14.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
15. 15.A cuboid is 7 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 17 cu cm (b) 182 cu cm (c) 21 cu cm (d) 147 cu cm
16. 16.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
17. 17.A cuboid is 9 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 332 sq cm (b) 664 sq cm (c) 360 sq cm (d) 166 sq cm
18. 18.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 484 sq cm (c) 121 sq cm (d) 1331 sq cm
19. 19.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 144 sq cm (d) 216 sq cm
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
22. 22.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
23. 23.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) 5 times (c) 2 times (d) 8 times
24. 24.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 132 sq cm (b) 80 sq cm (c) 264 sq cm (d) 66 sq cm
25. 25.A cuboid is 10 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 280 cu cm (b) 200 cu cm (c) 22 cu cm (d) 20 cu cm
26. 26.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
27. 27.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
28. 28.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
29. 29.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
30. 30.A cuboid is 10 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 608 sq cm (b) 320 sq cm (c) 152 sq cm (d) 304 sq cm
31. 31.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 8 cu cm (d) 24 cu cm
32. 32.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) 125 times (c) 5 times (d) 10 times
33. 33.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
35. 35.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 600 sq cm (c) 400 sq cm (d) 1000 sq cm
36. 36.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
37. 37.A cuboid is 10 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 210 cu cm (b) 20 cu cm (c) 30 cu cm (d) 242 cu cm
38. 38.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
39. 39.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
40. 40.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 10 cu cm (b) 13 cu cm (c) 104 cu cm (d) 60 cu cm

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