Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 189 · 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.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
2. 2.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) 8 times (c) 6 times (d) 2 times
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
5. 5.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) 25 times (d) 10 times
6. 6.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
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
8. 8.A cuboid is 8 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 176 sq cm (b) 448 sq cm (c) 704 sq cm (d) 352 sq cm
9. 9.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) 27 times (c) 3 times (d) 9 times
10. 10.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) 27 times (c) 9 times (d) 3 times
11. 11.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
12. 12.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
14. 14.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
17. 17.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 27 cu cm (c) 324 cu cm (d) 486 cu cm
18. 18.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 40 sq cm (b) 152 sq cm (c) 76 sq cm (d) 38 sq cm
19. 19.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 217 cu cm (d) 216 cu cm
20. 20.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
21. 21.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 40 cu cm (b) 17 cu cm (c) 8 cu cm (d) 16 cu cm
22. 22.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) 5 times (c) 2 times (d) 4 times
23. 23.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
24. 24.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
25. 25.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
26. 26.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 8 sq cm (d) 24 sq cm
27. 27.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
28. 28.A cuboid is 9 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 88 sq cm (b) 144 sq cm (c) 176 sq cm (d) 352 sq cm
29. 29.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
30. 30.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 125 sq cm (d) 100 sq cm
31. 31.A cuboid is 8 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 104 sq cm (b) 416 sq cm (c) 192 sq cm (d) 208 sq cm
32. 32.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
33. 33.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 76 sq cm (b) 40 sq cm (c) 38 sq cm (d) 152 sq cm
34. 34.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
35. 35.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
36. 36.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
37. 37.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
38. 38.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 73 sq cm (b) 36 sq cm (c) 72 sq cm (d) 144 sq cm
39. 39.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 16 sq cm (d) 96 sq cm
40. 40.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 144 sq cm (d) 36 sq cm

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