Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 609 · 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 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 96 sq cm (d) 97 sq cm
2. 2.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
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
4. 4.A cuboid is 6 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 13 cu cm (b) 104 cu cm (c) 60 cu cm (d) 12 cu cm
5. 5.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
6. 6.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
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
8. 8.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
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
10. 10.A cuboid is 10 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 304 sq cm (b) 152 sq cm (c) 608 sq cm (d) 320 sq cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
12. 12.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
14. 14.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
15. 15.A cuboid is 9 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 45 cu cm (b) 20 cu cm (c) 270 cu cm (d) 258 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) 8 times (c) 4 times (d) 5 times
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.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) 6 times (c) 27 times (d) 9 times
19. 19.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
20. 20.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
21. 21.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
22. 22.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 256 cu cm (d) 24 cu cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
25. 25.A cuboid is 10 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 536 sq cm (b) 134 sq cm (c) 240 sq cm (d) 268 sq cm
26. 26.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 216 cu cm (d) 217 cu cm
27. 27.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) 3 times (c) 6 times (d) 9 times
28. 28.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
29. 29.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 120 sq cm (b) 148 sq cm (c) 74 sq cm (d) 296 sq cm
30. 30.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 10 cu cm (b) 17 cu cm (c) 160 cu cm (d) 100 cu cm
31. 31.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
32. 32.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
33. 33.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 36 sq cm (c) 27 sq cm (d) 54 sq cm
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
35. 35.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
36. 36.A cuboid is 6 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 63 sq cm (b) 252 sq cm (c) 90 sq cm (d) 126 sq cm
37. 37.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
38. 38.A cuboid is 11 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 514 cu cm (b) 28 cu cm (c) 77 cu cm (d) 770 cu cm
39. 39.A cuboid is 8 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 314 sq cm (b) 360 sq cm (c) 628 sq cm (d) 157 sq cm
40. 40.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 24 sq cm (d) 8 sq cm

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