Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 291 · 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.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 36 cu cm (d) 27 cu cm
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
3. 3.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
4. 4.If the side of a square 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
5. 5.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
7. 7.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 576 cu cm
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
11. 11.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 486 cu cm (d) 324 cu cm
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
14. 14.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
15. 15.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
17. 17.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) 125 times (c) 10 times (d) 25 times
18. 18.A cuboid is 6 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 210 cu cm (b) 18 cu cm (c) 214 cu cm (d) 30 cu cm
19. 19.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
20. 20.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
22. 22.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
23. 23.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 30 cu cm
24. 24.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 96 cu cm (c) 65 cu cm (d) 12 cu cm
25. 25.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) 5 times (c) 25 times (d) 10 times
26. 26.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 576 sq cm (c) 144 sq cm (d) 864 sq cm
27. 27.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) 6 times (c) 4 times (d) 8 times
28. 28.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 4 sq cm (d) 24 sq cm
29. 29.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 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) 6 times (b) 9 times (c) 3 times (d) 27 times
31. 31.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 33 cu cm (c) 484 cu cm (d) 1331 cu 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) 8 times (c) 16 times (d) 64 times
33. 33.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 18 cu cm (b) 90 cu cm (c) 12 cu cm (d) 54 cu cm
34. 34.A cuboid is 10 cm long, 9 cm wide and 3 cm high. What is its volume? (a) 22 cu cm (b) 90 cu cm (c) 270 cu cm (d) 294 cu cm
35. 35.A cuboid is 11 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 290 sq cm (b) 264 sq cm (c) 145 sq cm (d) 580 sq cm
36. 36.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
37. 37.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
38. 38.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
39. 39.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) 8 times (c) 16 times (d) 64 times
40. 40.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 97 sq cm (d) 16 sq cm

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