Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 59 · 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 area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
2. 2.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
3. 3.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 76 cu cm (b) 40 cu cm (c) 11 cu cm (d) 8 cu cm
4. 4.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
7. 7.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
9. 9.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) 5 times (c) 125 times (d) 10 times
10. 10.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 64 cu cm (c) 65 cu cm (d) 96 cu cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
12. 12.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) 9 times (c) 3 times (d) 27 times
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
15. 15.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
16. 16.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
17. 17.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 216 sq cm (d) 217 sq cm
18. 18.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) 4 times (d) 8 times
19. 19.A cuboid is 7 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 56 sq cm (b) 200 sq cm (c) 100 sq cm (d) 50 sq cm
20. 20.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
21. 21.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 294 sq cm (d) 49 sq cm
22. 22.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
23. 23.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 64 sq cm (d) 96 sq cm
24. 24.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) 6 times (c) 2 times (d) 8 times
25. 25.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 40 sq cm (b) 80 sq cm (c) 48 sq cm (d) 160 sq cm
26. 26.A cuboid is 6 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 208 cu cm (b) 18 cu cm (c) 24 cu cm (d) 192 cu cm
27. 27.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) 64 times (c) 8 times (d) 4 times
28. 28.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
29. 29.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) 4 times (d) 64 times
30. 30.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
31. 31.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
32. 32.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 6 cu cm (b) 42 cu cm (c) 8 cu cm (d) 18 cu cm
33. 33.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) 5 times (c) 25 times (d) 10 times
34. 34.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 486 cu cm (d) 324 cu cm
35. 35.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
36. 36.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
37. 37.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 132 cu cm (b) 80 cu cm (c) 15 cu cm (d) 10 cu cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 10 cu cm (b) 50 cu cm (c) 12 cu cm (d) 90 cu cm
39. 39.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 12 sq cm (d) 32 sq cm
40. 40.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm

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