Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 293 · 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 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
4. 4.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
6. 6.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
7. 7.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 16 sq cm (c) 64 sq cm (d) 97 sq cm
8. 8.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
9. 9.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) 25 times (d) 10 times
10. 10.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 8 cu cm (d) 6 cu cm
11. 11.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
13. 13.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) 8 times (c) 16 times (d) 4 times
14. 14.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
15. 15.A cuboid is 8 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 340 cu cm (b) 23 cu cm (c) 400 cu cm (d) 40 cu 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) 2 times (b) 8 times (c) 4 times (d) 5 times
17. 17.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 726 sq cm (d) 484 sq cm
18. 18.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) 4 times (c) 16 times (d) 64 times
19. 19.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
20. 20.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 256 cu cm (d) 512 cu cm
21. 21.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 54 sq cm (d) 9 sq cm
22. 22.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
25. 25.A cuboid is 9 cm long, 8 cm wide and 2 cm high. What is its volume? (a) 212 cu cm (b) 144 cu cm (c) 19 cu cm (d) 72 cu cm
26. 26.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 68 sq cm (b) 272 sq cm (c) 96 sq cm (d) 136 sq cm
27. 27.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
28. 28.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
29. 29.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 150 cu cm (d) 100 cu cm
30. 30.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
31. 31.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 96 cu cm (d) 12 cu cm
32. 32.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
33. 33.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 32 sq cm (b) 128 sq cm (c) 65 sq cm (d) 64 sq cm
34. 34.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
35. 35.A cuboid is 6 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 208 sq cm (b) 416 sq cm (c) 192 sq cm (d) 104 sq cm
36. 36.A cuboid is 7 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 240 cu cm (b) 42 cu cm (c) 19 cu cm (d) 252 cu cm
37. 37.A cuboid is 5 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 184 cu cm (b) 17 cu cm (c) 20 cu cm (d) 160 cu cm
38. 38.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 9 cu cm (d) 54 cu cm
39. 39.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) 6 times (d) 27 times
40. 40.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm

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