Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 734 · 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 the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
2. 2.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
3. 3.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
4. 4.A cuboid is 9 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 140 sq cm (b) 280 sq cm (c) 288 sq cm (d) 560 sq cm
5. 5.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
6. 6.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
7. 7.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
8. 8.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
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
10. 10.A cuboid is 6 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 126 sq cm (b) 63 sq cm (c) 252 sq cm (d) 90 sq cm
11. 11.A cuboid is 8 cm long, 7 cm wide and 10 cm high. What is its total surface area? (a) 560 sq cm (b) 412 sq cm (c) 206 sq cm (d) 824 sq cm
12. 12.A cuboid is 12 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 52 sq cm (b) 48 sq cm (c) 104 sq cm (d) 208 sq cm
13. 13.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
14. 14.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
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
16. 16.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 100 sq cm (d) 600 sq cm
17. 17.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) 6 times (c) 3 times (d) 9 times
18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
19. 19.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
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
21. 21.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 84 sq cm (c) 42 sq cm (d) 21 sq cm
22. 22.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
23. 23.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 726 sq cm (c) 121 sq cm (d) 1331 sq cm
24. 24.A cuboid is 8 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 12 cu cm (b) 16 cu cm (c) 32 cu cm (d) 72 cu cm
25. 25.A cuboid is 7 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 344 sq cm (b) 112 sq cm (c) 172 sq cm (d) 86 sq cm
26. 26.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
28. 28.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 380 sq cm (b) 95 sq cm (c) 190 sq cm (d) 150 sq cm
29. 29.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
30. 30.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
31. 31.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 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) 4 times (b) 64 times (c) 16 times (d) 8 times
33. 33.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
34. 34.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
35. 35.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) 5 times (c) 25 times (d) 125 times
36. 36.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 384 cu cm (d) 256 cu cm
37. 37.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 150 cu cm (c) 100 cu cm (d) 15 cu cm
38. 38.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
39. 39.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) 4 times (c) 6 times (d) 8 times
40. 40.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) 10 times (c) 125 times (d) 25 times

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