Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 230 · 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 cuboid is 10 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 552 sq cm (b) 138 sq cm (c) 280 sq cm (d) 276 sq cm
2. 2.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
3. 3.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 400 cu cm
4. 4.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 124 sq cm (b) 496 sq cm (c) 248 sq cm (d) 240 sq cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
7. 7.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
8. 8.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
9. 9.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 16 sq cm (d) 24 sq cm
10. 10.A cuboid is 11 cm long, 10 cm wide and 4 cm high. What is its total surface area? (a) 194 sq cm (b) 440 sq cm (c) 388 sq cm (d) 776 sq cm
11. 11.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 25 sq cm (d) 150 sq cm
12. 12.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) 4 times (c) 8 times (d) 64 times
13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
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) 4 times (b) 5 times (c) 2 times (d) 8 times
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
17. 17.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
19. 19.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 484 cu cm
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
21. 21.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 8 cu cm (b) 88 cu cm (c) 48 cu cm (d) 12 cu cm
22. 22.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
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
24. 24.A cuboid is 10 cm long, 8 cm wide and 2 cm high. What is its total surface area? (a) 116 sq cm (b) 232 sq cm (c) 160 sq cm (d) 464 sq cm
25. 25.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) 16 times (d) 64 times
26. 26.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
27. 27.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
28. 28.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 1000 sq cm (c) 400 sq cm (d) 600 sq cm
29. 29.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
30. 30.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 15 cu cm (d) 125 cu cm
31. 31.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 24 cu cm (d) 16 cu cm
32. 32.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) 3 times (d) 6 times
33. 33.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
35. 35.A cuboid is 10 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 800 sq cm (b) 500 sq cm (c) 400 sq cm (d) 200 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) 25 times (b) 5 times (c) 10 times (d) 125 times
37. 37.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
38. 38.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 33 sq cm (b) 66 sq cm (c) 132 sq cm (d) 36 sq cm
39. 39.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 256 cu cm (d) 512 cu cm
40. 40.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 256 sq cm (c) 512 sq cm (d) 64 sq cm

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