Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 181 · 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) 125 times (b) 25 times (c) 10 times (d) 5 times
2. 2.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 47 sq cm (b) 60 sq cm (c) 94 sq cm (d) 188 sq cm
3. 3.If the radius of a circle 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.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
5. 5.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
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
7. 7.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) 9 times (d) 3 times
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
9. 9.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) 6 times (c) 27 times (d) 3 times
10. 10.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 18 cu cm (b) 6 cu cm (c) 8 cu cm (d) 42 cu cm
11. 11.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 30 cu cm
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
14. 14.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 74 sq cm (b) 148 sq cm (c) 296 sq cm (d) 120 sq cm
15. 15.A cuboid is 8 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 680 sq cm (b) 400 sq cm (c) 340 sq cm (d) 170 sq cm
16. 16.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) 5 times (d) 2 times
17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
19. 19.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
20. 20.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
22. 22.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
23. 23.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
25. 25.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
26. 26.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 217 cu cm (d) 144 cu cm
27. 27.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 512 cu cm (d) 24 cu cm
28. 28.If the radius of a circle 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
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
30. 30.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 729 sq cm (d) 324 sq cm
31. 31.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
32. 32.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) 4 times (c) 8 times (d) 16 times
33. 33.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) 8 times (c) 6 times (d) 2 times
34. 34.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 118 cu cm (b) 10 cu cm (c) 70 cu cm (d) 14 cu cm
35. 35.A cuboid is 8 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 32 sq cm (b) 144 sq cm (c) 36 sq cm (d) 72 sq cm
36. 36.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 65 cu cm (d) 12 cu cm
37. 37.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
38. 38.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
39. 39.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
40. 40.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 217 sq cm (c) 216 sq cm (d) 36 sq cm

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