Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 455 · 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 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 36 sq cm (d) 144 sq cm
2. 2.A cuboid is 9 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 144 cu cm (b) 17 cu cm (c) 176 cu cm (d) 36 cu cm
3. 3.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 144 sq cm (c) 864 sq cm (d) 576 sq cm
4. 4.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) 3 times (c) 9 times (d) 27 times
5. 5.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 101 sq cm (b) 168 sq cm (c) 202 sq cm (d) 404 sq cm
6. 6.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 36 sq cm (b) 72 sq cm (c) 73 sq cm (d) 144 sq cm
7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
8. 8.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
9. 9.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 4 sq cm (d) 8 sq cm
10. 10.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 10 cu cm (b) 20 cu cm (c) 9 cu cm (d) 48 cu cm
11. 11.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
12. 12.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
13. 13.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
15. 15.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
16. 16.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
17. 17.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) 6 times (c) 3 times (d) 27 times
18. 18.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) 4 times (c) 16 times (d) 64 times
19. 19.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 64 cu cm (d) 12 cu cm
20. 20.A cuboid is 8 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 40 cu cm (b) 22 cu cm (c) 360 cu cm (d) 314 cu cm
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
22. 22.A cuboid is 5 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 166 sq cm (b) 140 sq cm (c) 83 sq cm (d) 332 sq cm
23. 23.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
24. 24.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) 8 times (c) 4 times (d) 5 times
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
26. 26.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
27. 27.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
28. 28.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 125 cu cm (c) 150 cu cm (d) 15 cu cm
29. 29.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 400 sq cm (c) 100 sq cm (d) 600 sq cm
30. 30.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
31. 31.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 97 sq cm (d) 96 sq cm
32. 32.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
33. 33.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) 125 times (c) 10 times (d) 5 times
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
35. 35.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 125 sq cm (d) 100 sq cm
36. 36.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
37. 37.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
38. 38.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
39. 39.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
40. 40.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

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