Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 469 · 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 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 cu cm
2. 2.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) 9 times (d) 3 times
3. 3.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
4. 4.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 217 cu cm (d) 144 cu cm
5. 5.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) 10 times (d) 25 times
6. 6.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 576 cu cm (c) 1728 cu cm (d) 36 cu 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) 125 times (d) 10 times
8. 8.A cuboid is 7 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 208 cu cm (b) 14 cu cm (c) 19 cu cm (d) 140 cu cm
9. 9.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 6 cu cm (b) 18 cu cm (c) 42 cu cm (d) 8 cu cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
11. 11.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 97 sq cm (d) 96 sq cm
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
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) 6 times (d) 3 times
14. 14.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
15. 15.A cuboid is 12 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 192 sq cm (b) 768 sq cm (c) 432 sq cm (d) 384 sq cm
16. 16.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
17. 17.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
18. 18.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
19. 19.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 600 sq cm (d) 100 sq cm
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
22. 22.A cuboid is 10 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 300 sq cm (b) 320 sq cm (c) 640 sq cm (d) 160 sq cm
23. 23.A cuboid is 9 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 352 sq cm (b) 144 sq cm (c) 176 sq cm (d) 88 sq cm
24. 24.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
25. 25.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
26. 26.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
27. 27.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) 6 times (c) 3 times (d) 9 times
28. 28.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
29. 29.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
30. 30.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
31. 31.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) 4 times (c) 8 times (d) 64 times
32. 32.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
33. 33.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
34. 34.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
35. 35.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 125 sq cm (d) 150 sq cm
36. 36.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 256 cu cm (d) 384 cu cm
37. 37.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
38. 38.A cuboid is 11 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 234 cu cm (b) 33 cu cm (c) 198 cu cm (d) 20 cu cm
39. 39.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
40. 40.A cuboid is 11 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 33 cu cm (b) 66 cu cm (c) 122 cu cm (d) 16 cu cm

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