Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 508 · 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.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) 27 times (c) 6 times (d) 3 times
2. 2.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 48 sq cm (b) 184 sq cm (c) 46 sq cm (d) 92 sq cm
3. 3.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
4. 4.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 8 times (d) 6 times
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
7. 7.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
10. 10.A cuboid is 12 cm long, 8 cm wide and 10 cm high. What is its total surface area? (a) 1184 sq cm (b) 296 sq cm (c) 960 sq cm (d) 592 sq cm
11. 11.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) 27 times (d) 6 times
12. 12.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
13. 13.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) 25 times (d) 5 times
14. 14.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
15. 15.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 27 cu cm (d) 54 cu cm
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
17. 17.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
18. 18.A cuboid is 9 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 18 cu cm (b) 212 cu cm (c) 144 cu cm (d) 19 cu cm
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
20. 20.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
21. 21.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
22. 22.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
23. 23.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) 8 times (c) 16 times (d) 64 times
24. 24.A cuboid is 12 cm long, 10 cm wide and 4 cm high. What is its volume? (a) 26 cu cm (b) 480 cu cm (c) 120 cu cm (d) 416 cu cm
25. 25.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 64 sq cm (d) 97 sq cm
26. 26.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
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
28. 28.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 343 cu cm (d) 21 cu cm
29. 29.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 576 sq cm
30. 30.A cuboid is 10 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 60 cu cm (b) 184 cu cm (c) 18 cu cm (d) 120 cu cm
31. 31.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 248 sq cm (b) 124 sq cm (c) 72 sq cm (d) 62 sq cm
32. 32.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 324 cu cm (c) 486 cu cm (d) 27 cu cm
33. 33.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
34. 34.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) 10 times (d) 25 times
35. 35.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
36. 36.A cuboid is 12 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 160 cu cm (b) 18 cu cm (c) 24 cu cm (d) 96 cu cm
37. 37.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
38. 38.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 64 cu cm (d) 65 cu cm
39. 39.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
40. 40.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times

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