Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 591 · 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 6 cm. What is its total surface area? (a) 144 sq cm (b) 216 sq cm (c) 36 sq cm (d) 217 sq cm
2. 2.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
4. 4.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
6. 6.A cuboid is 7 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 210 sq cm (b) 105 sq cm (c) 196 sq cm (d) 420 sq cm
7. 7.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
8. 8.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 15 cu cm (d) 100 cu cm
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
10. 10.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
11. 11.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
12. 12.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 24 sq cm (b) 26 sq cm (c) 52 sq cm (d) 104 sq cm
13. 13.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
14. 14.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 30 cu cm
15. 15.A cuboid is 6 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 28 sq cm (b) 56 sq cm (c) 112 sq cm (d) 24 sq cm
16. 16.A cuboid is 9 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 324 sq cm (b) 288 sq cm (c) 144 sq cm (d) 576 sq cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
19. 19.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 27 sq cm (c) 36 sq cm (d) 9 sq cm
20. 20.A cuboid is 12 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 768 sq cm (b) 192 sq cm (c) 432 sq cm (d) 384 sq cm
21. 21.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 8 sq cm (d) 4 sq cm
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
23. 23.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
25. 25.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
26. 26.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) 9 times (c) 3 times (d) 27 times
27. 27.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
29. 29.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) 25 times (c) 125 times (d) 10 times
30. 30.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 80 cu cm (b) 8 cu cm (c) 16 cu cm (d) 136 cu cm
31. 31.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
32. 32.A cuboid is 11 cm long, 7 cm wide and 7 cm high. What is its total surface area? (a) 812 sq cm (b) 539 sq cm (c) 203 sq cm (d) 406 sq cm
33. 33.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 24 cu cm (b) 9 cu cm (c) 8 cu cm (d) 52 cu cm
34. 34.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
35. 35.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 54 cu cm (d) 27 cu cm
36. 36.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) 8 times (d) 2 times
37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
38. 38.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) 25 times (c) 125 times (d) 5 times
39. 39.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 10 cu cm (c) 9 cu cm (d) 20 cu cm
40. 40.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) 16 times (d) 8 times

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