Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 414 · 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.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
2. 2.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
3. 3.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
6. 6.A cuboid is 10 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 100 cu cm (b) 160 cu cm (c) 17 cu cm (d) 50 cu cm
7. 7.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
8. 8.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
9. 9.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
10. 10.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
11. 11.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
12. 12.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 202 sq cm (b) 101 sq cm (c) 404 sq cm (d) 168 sq cm
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
14. 14.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) 27 times (c) 9 times (d) 3 times
15. 15.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 30 cu cm (d) 400 cu cm
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
17. 17.A cuboid is 8 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 48 sq cm (b) 46 sq cm (c) 184 sq cm (d) 92 sq cm
18. 18.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 16 sq cm (c) 97 sq cm (d) 64 sq cm
19. 19.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
20. 20.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
21. 21.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
23. 23.A cuboid is 6 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 49 cu cm (b) 48 cu cm (c) 88 cu cm (d) 12 cu cm
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
25. 25.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) 4 times (c) 8 times (d) 5 times
26. 26.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 96 cu cm (c) 65 cu cm (d) 12 cu cm
27. 27.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
28. 28.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) 27 times (d) 9 times
29. 29.A cuboid is 8 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 120 sq cm (b) 316 sq cm (c) 79 sq cm (d) 158 sq cm
30. 30.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 25 sq cm (c) 100 sq cm (d) 150 sq cm
31. 31.A cuboid is 8 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 128 cu cm (b) 16 cu cm (c) 192 cu cm (d) 18 cu cm
32. 32.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
33. 33.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 217 cu cm (d) 216 cu cm
34. 34.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 486 cu cm (c) 324 cu cm (d) 27 cu cm
35. 35.A cuboid is 12 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 256 cu cm (b) 240 cu cm (c) 48 cu cm (d) 21 cu cm
36. 36.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
37. 37.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
38. 38.A cuboid is 8 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 132 cu cm (b) 15 cu cm (c) 40 cu cm (d) 80 cu 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) 8 times (b) 64 times (c) 4 times (d) 16 times
40. 40.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 73 sq cm (d) 72 sq cm

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