Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 2 · 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 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 48 sq cm (b) 176 sq cm (c) 44 sq cm (d) 88 sq cm
2. 2.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
3. 3.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
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 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) 5 times (b) 25 times (c) 10 times (d) 125 times
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
9. 9.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 33 cu cm (c) 1331 cu cm (d) 484 cu cm
10. 10.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 10 cu cm (b) 80 cu cm (c) 15 cu cm (d) 132 cu cm
11. 11.A cuboid is 8 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 368 sq cm (b) 92 sq cm (c) 160 sq cm (d) 184 sq cm
12. 12.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 40 sq cm (c) 20 sq cm (d) 80 sq cm
13. 13.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
14. 14.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) 64 times (d) 16 times
15. 15.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
16. 16.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 32 cu cm (b) 12 cu cm (c) 7 cu cm (d) 6 cu cm
18. 18.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) 4 times (d) 5 times
19. 19.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
20. 20.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) 16 times (d) 4 times
21. 21.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
22. 22.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
23. 23.A cuboid is 10 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 368 sq cm (b) 120 sq cm (c) 184 sq cm (d) 92 sq cm
24. 24.A cuboid is 10 cm long, 9 cm wide and 7 cm high. What is its total surface area? (a) 446 sq cm (b) 223 sq cm (c) 630 sq cm (d) 892 sq cm
25. 25.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
26. 26.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
27. 27.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 6 times (d) 8 times
28. 28.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 27 sq cm (d) 36 sq cm
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
30. 30.A cuboid is 8 cm long, 7 cm wide and 5 cm high. What is its total surface area? (a) 524 sq cm (b) 131 sq cm (c) 262 sq cm (d) 280 sq cm
31. 31.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 256 cu cm (d) 512 cu cm
32. 32.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
33. 33.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
34. 34.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
35. 35.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 16 cu cm (b) 40 cu cm (c) 8 cu cm (d) 17 cu cm
36. 36.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
37. 37.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
38. 38.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
39. 39.A cuboid is 11 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 238 cu cm (b) 220 cu cm (c) 55 cu cm (d) 20 cu cm
40. 40.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

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