Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 19 · 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 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
2. 2.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
3. 3.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
4. 4.A cuboid is 12 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 60 cu cm (b) 358 cu cm (c) 24 cu cm (d) 420 cu cm
5. 5.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
6. 6.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 72 cu cm (b) 18 cu cm (c) 36 cu cm (d) 11 cu cm
7. 7.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 576 sq cm
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
10. 10.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 96 sq cm (d) 64 sq cm
11. 11.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
14. 14.A cuboid is 10 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 124 sq cm (b) 240 sq cm (c) 248 sq cm (d) 496 sq cm
15. 15.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 492 sq cm (b) 246 sq cm (c) 216 sq cm (d) 123 sq cm
16. 16.A cuboid is 10 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 300 sq cm (b) 160 sq cm (c) 640 sq cm (d) 320 sq cm
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) 8 times (b) 64 times (c) 16 times (d) 4 times
18. 18.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
19. 19.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 64 sq cm (c) 256 sq cm (d) 384 sq cm
20. 20.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 64 cu cm (d) 96 cu cm
21. 21.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 16 cu cm (d) 8 cu cm
22. 22.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
23. 23.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 484 sq cm (c) 726 sq cm (d) 121 sq cm
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
26. 26.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
27. 27.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 150 sq cm (c) 100 sq cm (d) 25 sq cm
28. 28.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
29. 29.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
30. 30.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
31. 31.A cuboid is 10 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 90 cu cm (b) 332 cu cm (c) 23 cu cm (d) 360 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) 693 sq cm (d) 5544 sq cm
33. 33.A cuboid is 10 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 40 cu cm (b) 120 cu cm (c) 164 cu cm (d) 17 cu cm
34. 34.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
35. 35.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
36. 36.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 380 sq cm (b) 190 sq cm (c) 150 sq cm (d) 95 sq cm
37. 37.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
38. 38.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
39. 39.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 27 cu cm (c) 729 cu cm (d) 486 cu cm
40. 40.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 36 sq cm (d) 9 sq cm

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