Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 657 · 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.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) 8 times (c) 5 times (d) 2 times
2. 2.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) 64 times (c) 4 times (d) 8 times
3. 3.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 15 cu cm (b) 80 cu cm (c) 132 cu cm (d) 10 cu cm
4. 4.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq 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) 10 times (b) 125 times (c) 25 times (d) 5 times
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
7. 7.A cuboid is 10 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 100 sq cm (b) 80 sq cm (c) 320 sq cm (d) 160 sq 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) 16 times (b) 64 times (c) 4 times (d) 8 times
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
10. 10.A cuboid is 10 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 120 sq cm (b) 92 sq cm (c) 368 sq cm (d) 184 sq cm
11. 11.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
13. 13.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 180 sq cm (b) 45 sq cm (c) 54 sq cm (d) 90 sq cm
14. 14.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 8 sq cm (d) 24 sq cm
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq 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) 25 times (b) 10 times (c) 5 times (d) 125 times
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
18. 18.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
19. 19.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
20. 20.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
21. 21.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 8 times (c) 6 times (d) 4 times
22. 22.A cuboid is 6 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 236 cu cm (b) 30 cu cm (c) 240 cu cm (d) 19 cu cm
23. 23.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 256 sq cm (d) 512 sq cm
24. 24.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
25. 25.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 864 sq cm
26. 26.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 54 sq cm (b) 204 sq cm (c) 102 sq cm (d) 51 sq cm
27. 27.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 150 cu cm (b) 190 cu cm (c) 18 cu cm (d) 15 cu cm
28. 28.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
30. 30.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 25 sq cm (d) 125 sq cm
31. 31.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq 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) 3 times (b) 9 times (c) 6 times (d) 27 times
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
34. 34.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
35. 35.A cuboid is 8 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 72 sq cm (b) 114 sq cm (c) 57 sq cm (d) 228 sq cm
36. 36.A cuboid is 6 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 208 sq cm (b) 52 sq cm (c) 60 sq cm (d) 104 sq cm
37. 37.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 292 sq cm (b) 90 sq cm (c) 146 sq cm (d) 73 sq cm
38. 38.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
39. 39.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 27 cu cm (d) 54 cu cm
40. 40.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm

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