Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 357 · 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 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 27 sq cm (d) 9 sq cm
2. 2.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
3. 3.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 400 cu cm (d) 600 cu cm
4. 4.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 70 cu cm (b) 14 cu cm (c) 118 cu cm (d) 10 cu cm
5. 5.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
6. 6.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
7. 7.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
8. 8.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) 4 times (c) 2 times (d) 5 times
9. 9.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 46 sq cm (b) 184 sq cm (c) 92 sq cm (d) 48 sq cm
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
11. 11.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
12. 12.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
13. 13.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 125 cu cm (c) 15 cu cm (d) 150 cu cm
14. 14.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 40 cu cm (b) 16 cu cm (c) 8 cu cm (d) 17 cu cm
15. 15.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 56 sq cm (b) 50 sq cm (c) 100 sq cm (d) 200 sq cm
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
17. 17.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
18. 18.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 188 sq cm (b) 47 sq cm (c) 94 sq cm (d) 60 sq cm
19. 19.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
20. 20.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
21. 21.A cuboid is 8 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 560 sq cm (b) 288 sq cm (c) 280 sq cm (d) 140 sq 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 10 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 304 cu cm (b) 22 cu cm (c) 40 cu cm (d) 320 cu cm
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
25. 25.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
26. 26.A cuboid is 10 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 720 sq cm (b) 400 sq cm (c) 180 sq cm (d) 360 sq cm
27. 27.A cuboid is 7 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 21 cu cm (b) 82 cu cm (c) 42 cu cm (d) 12 cu cm
28. 28.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
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
30. 30.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
31. 31.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
32. 32.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) 5 times (c) 4 times (d) 8 times
33. 33.A cuboid is 9 cm long, 8 cm wide and 10 cm high. What is its volume? (a) 720 cu cm (b) 484 cu cm (c) 72 cu cm (d) 27 cu cm
34. 34.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
35. 35.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
36. 36.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
37. 37.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 150 sq cm (d) 25 sq cm
38. 38.A cuboid is 6 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 30 cu cm (b) 170 cu cm (c) 16 cu cm (d) 150 cu cm
39. 39.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
40. 40.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 78 cu cm (b) 11 cu cm (c) 15 cu cm (d) 45 cu cm

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