Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 634 · 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 radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
3. 3.A cuboid is 7 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 21 cu cm (b) 336 cu cm (c) 292 cu cm (d) 42 cu cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
5. 5.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
6. 6.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
7. 7.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 729 sq cm (d) 486 sq cm
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq 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) 616 cm (d) 44 cm
12. 12.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) 5 times (c) 4 times (d) 8 times
13. 13.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
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) 6 times (c) 3 times (d) 9 times
15. 15.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) 8 times (c) 5 times (d) 4 times
16. 16.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
17. 17.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 21 cu cm (d) 294 cu cm
18. 18.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
19. 19.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
21. 21.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
22. 22.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 6 times (d) 4 times
26. 26.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 24 cu cm (b) 9 cu cm (c) 52 cu cm (d) 8 cu cm
27. 27.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 100 sq cm (d) 600 sq cm
28. 28.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 88 sq cm (b) 48 sq cm (c) 44 sq cm (d) 176 sq cm
29. 29.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
30. 30.A cuboid is 11 cm long, 8 cm wide and 8 cm high. What is its volume? (a) 88 cu cm (b) 27 cu cm (c) 480 cu cm (d) 704 cu cm
31. 31.A cuboid is 6 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 120 cu cm (b) 148 cu cm (c) 15 cu cm (d) 30 cu cm
32. 32.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
33. 33.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
34. 34.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
35. 35.A cuboid is 6 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 16 cu cm (b) 144 cu cm (c) 24 cu cm (d) 168 cu cm
36. 36.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 256 cu cm (d) 512 cu cm
37. 37.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
38. 38.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 27 cu cm (c) 486 cu cm (d) 729 cu cm
39. 39.A cuboid is 10 cm long, 9 cm wide and 2 cm high. What is its total surface area? (a) 512 sq cm (b) 128 sq cm (c) 180 sq cm (d) 256 sq cm
40. 40.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times

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