Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 413 · 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 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
2. 2.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 50 sq cm (b) 100 sq cm (c) 200 sq cm (d) 56 sq cm
3. 3.A cuboid is 6 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 108 sq cm (b) 54 sq cm (c) 216 sq cm (d) 72 sq cm
4. 4.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 294 cu cm (d) 21 cu cm
5. 5.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
6. 6.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) 6 times (c) 27 times (d) 9 times
7. 7.A cuboid is 10 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 95 sq cm (b) 380 sq cm (c) 150 sq cm (d) 190 sq cm
8. 8.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
9. 9.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
11. 11.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) 9 times (c) 27 times (d) 6 times
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
14. 14.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
15. 15.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
16. 16.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
17. 17.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
18. 18.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
19. 19.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
20. 20.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
21. 21.A cuboid is 12 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 384 cu cm (b) 108 cu cm (c) 25 cu cm (d) 432 cu cm
22. 22.A cuboid is 9 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 13 cu cm (b) 36 cu cm (c) 18 cu cm (d) 80 cu cm
23. 23.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
24. 24.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 36 sq cm (d) 217 sq cm
25. 25.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 97 sq cm (d) 96 sq cm
26. 26.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) 5 times (d) 125 times
27. 27.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 9 cu cm (c) 54 cu cm (d) 36 cu cm
28. 28.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 576 sq cm
29. 29.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 13 cu cm (b) 48 cu cm (c) 6 cu cm (d) 92 cu cm
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
31. 31.A cuboid is 8 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 18 cu cm (b) 192 cu cm (c) 208 cu cm (d) 48 cu cm
32. 32.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) 5 times (c) 25 times (d) 125 times
33. 33.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
34. 34.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
36. 36.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
37. 37.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 726 cu cm (d) 1331 cu cm
38. 38.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 15 cu cm (b) 60 cu cm (c) 94 cu cm (d) 12 cu cm
39. 39.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
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm

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