Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 767 · 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 volume? (a) 96 cu cm (b) 64 cu cm (c) 65 cu cm (d) 12 cu cm
2. 2.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 36 cu cm (c) 576 cu cm (d) 864 cu cm
3. 3.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
4. 4.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 20 sq cm (b) 40 sq cm (c) 16 sq cm (d) 80 sq cm
5. 5.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
8. 8.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
10. 10.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 484 sq cm (d) 726 sq cm
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
12. 12.A cuboid is 11 cm long, 7 cm wide and 3 cm high. What is its total surface area? (a) 131 sq cm (b) 262 sq cm (c) 524 sq cm (d) 231 sq cm
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
14. 14.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
15. 15.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 16 cu cm (b) 126 cu cm (c) 42 cu cm (d) 162 cu cm
16. 16.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
18. 18.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
19. 19.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 24 cu cm (b) 12 cu cm (c) 88 cu cm (d) 48 cu cm
20. 20.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
21. 21.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 216 cu cm (b) 24 cu cm (c) 19 cu cm (d) 228 cu cm
22. 22.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 324 sq cm (d) 729 sq cm
23. 23.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
24. 24.A cuboid is 11 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 430 cu cm (b) 55 cu cm (c) 26 cu cm (d) 550 cu cm
25. 25.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
26. 26.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
27. 27.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) 4 times (c) 5 times (d) 8 times
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
29. 29.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
30. 30.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
31. 31.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
32. 32.A cuboid is 5 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 202 cu cm (b) 20 cu cm (c) 18 cu cm (d) 180 cu cm
33. 33.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
34. 34.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
35. 35.A cuboid is 12 cm long, 9 cm wide and 8 cm high. What is its total surface area? (a) 864 sq cm (b) 276 sq cm (c) 1104 sq cm (d) 552 sq cm
36. 36.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 6 cu cm (b) 10 cu cm (c) 62 cu cm (d) 30 cu cm
37. 37.A cuboid is 11 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 352 cu cm (b) 23 cu cm (c) 44 cu cm (d) 328 cu cm
38. 38.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
39. 39.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
40. 40.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 440 sq cm (b) 110 sq cm (c) 220 sq cm (d) 200 sq cm

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