Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 507 · 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 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
3. 3.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
4. 4.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) 2 times (c) 5 times (d) 4 times
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
7. 7.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
10. 10.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
11. 11.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
12. 12.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 172 cu cm (b) 17 cu cm (c) 56 cu cm (d) 112 cu cm
13. 13.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
14. 14.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
15. 15.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 196 cu cm (d) 21 cu cm
16. 16.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) 8 times (d) 4 times
17. 17.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
18. 18.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) 64 times (c) 16 times (d) 4 times
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
20. 20.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) 4 times (c) 64 times (d) 8 times
21. 21.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
22. 22.A cuboid is 11 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 358 cu cm (b) 24 cu cm (c) 396 cu cm (d) 99 cu cm
23. 23.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
24. 24.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 486 sq cm (c) 81 sq cm (d) 324 sq cm
25. 25.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 64 cu cm (b) 112 cu cm (c) 14 cu cm (d) 8 cu cm
26. 26.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
27. 27.A cuboid is 9 cm long, 7 cm wide and 6 cm high. What is its volume? (a) 378 cu cm (b) 318 cu cm (c) 63 cu cm (d) 22 cu cm
28. 28.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) 4 times (c) 6 times (d) 8 times
29. 29.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 8 cu cm (d) 16 cu cm
30. 30.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) 5 times (c) 4 times (d) 8 times
31. 31.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
32. 32.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
33. 33.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 125 cu cm (d) 15 cu cm
34. 34.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
35. 35.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 104 sq cm (b) 52 sq cm (c) 26 sq cm (d) 24 sq cm
36. 36.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) 25 times (c) 10 times (d) 5 times
37. 37.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) 10 times (c) 125 times (d) 25 times
38. 38.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
39. 39.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) 6 times (c) 9 times (d) 27 times
40. 40.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 100 sq cm (d) 125 sq cm

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