Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 986 · 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 every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
4. 4.A cuboid is 9 cm long, 7 cm wide and 10 cm high. What is its total surface area? (a) 446 sq cm (b) 630 sq cm (c) 892 sq cm (d) 223 sq cm
5. 5.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) 5 times (c) 125 times (d) 25 times
6. 6.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 217 cu cm (c) 18 cu cm (d) 144 cu cm
7. 7.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
8. 8.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 21 cu cm (c) 294 cu cm (d) 196 cu cm
9. 9.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
10. 10.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) 8 times (c) 4 times (d) 5 times
11. 11.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 120 sq cm (b) 74 sq cm (c) 148 sq cm (d) 296 sq cm
12. 12.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 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) 8 times (b) 16 times (c) 4 times (d) 64 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) 27 times (b) 3 times (c) 9 times (d) 6 times
15. 15.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 486 sq cm (c) 81 sq cm (d) 729 sq cm
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
17. 17.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) 8 times (c) 64 times (d) 16 times
18. 18.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
19. 19.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
20. 20.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) 8 times (c) 4 times (d) 5 times
21. 21.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 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) 3 times (b) 6 times (c) 27 times (d) 9 times
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
24. 24.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
25. 25.A cuboid is 12 cm long, 9 cm wide and 2 cm high. What is its total surface area? (a) 600 sq cm (b) 216 sq cm (c) 300 sq cm (d) 150 sq cm
26. 26.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
27. 27.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 6 cu cm (b) 13 cu cm (c) 48 cu cm (d) 92 cu cm
28. 28.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
29. 29.A cuboid is 8 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 264 sq cm (b) 66 sq cm (c) 80 sq cm (d) 132 sq cm
30. 30.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) 6 times (c) 8 times (d) 4 times
31. 31.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 24 cu cm (d) 384 cu cm
32. 32.A cuboid is 12 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 289 cu cm (b) 288 cu cm (c) 22 cu cm (d) 48 cu cm
33. 33.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
34. 34.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
35. 35.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) 125 times (c) 10 times (d) 25 times
36. 36.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 108 sq cm (b) 81 sq cm (c) 162 sq cm (d) 324 sq cm
37. 37.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
38. 38.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 72 sq cm (b) 73 sq cm (c) 144 sq cm (d) 36 sq cm
39. 39.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) 27 times (c) 6 times (d) 9 times
40. 40.A cuboid is 12 cm long, 11 cm wide and 10 cm high. What is its volume? (a) 724 cu cm (b) 33 cu cm (c) 1320 cu cm (d) 132 cu cm

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