Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 29 · 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.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
2. 2.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
3. 3.If the radius of a circle 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
4. 4.A cuboid is 10 cm long, 8 cm wide and 10 cm high. What is its total surface area? (a) 800 sq cm (b) 520 sq cm (c) 260 sq cm (d) 1040 sq cm
5. 5.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 400 sq cm (c) 1000 sq cm (d) 100 sq cm
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
7. 7.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
8. 8.A cuboid is 10 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 18 cu cm (b) 40 cu cm (c) 160 cu cm (d) 192 cu cm
9. 9.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) 64 times (c) 8 times (d) 4 times
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
11. 11.A cuboid is 5 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 404 sq cm (b) 101 sq cm (c) 202 sq cm (d) 180 sq cm
12. 12.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
13. 13.A cuboid is 10 cm long, 8 cm wide and 9 cm high. What is its volume? (a) 80 cu cm (b) 27 cu cm (c) 484 cu cm (d) 720 cu cm
14. 14.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
16. 16.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
17. 17.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 15 cu cm (b) 136 cu cm (c) 96 cu cm (d) 12 cu cm
18. 18.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 512 sq cm (c) 256 sq cm (d) 64 sq cm
19. 19.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
20. 20.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) 27 times (c) 9 times (d) 3 times
21. 21.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
22. 22.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) 9 times (d) 27 times
23. 23.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) 125 times (d) 25 times
24. 24.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
25. 25.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 96 sq cm (d) 64 sq cm
26. 26.A cuboid is 12 cm long, 11 cm wide and 5 cm high. What is its volume? (a) 494 cu cm (b) 660 cu cm (c) 132 cu cm (d) 28 cu cm
27. 27.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
28. 28.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
29. 29.If the radius of a circle 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
30. 30.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 216 cu cm (b) 19 cu cm (c) 18 cu cm (d) 180 cu cm
31. 31.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
32. 32.A cuboid is 11 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 66 cu cm (b) 528 cu cm (c) 404 cu cm (d) 25 cu cm
33. 33.A cuboid is 10 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 200 sq cm (b) 400 sq cm (c) 800 sq cm (d) 500 sq cm
34. 34.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
35. 35.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 256 cu cm (d) 384 cu cm
36. 36.A cuboid is 12 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 66 sq cm (b) 264 sq cm (c) 72 sq cm (d) 132 sq cm
37. 37.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) 16 times (d) 8 times
38. 38.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
39. 39.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 15 cu cm (c) 150 cu cm (d) 125 cu cm
40. 40.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 6 cu cm (b) 18 cu cm (c) 8 cu cm (d) 42 cu cm

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