Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 785 · 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 radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
2. 2.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
3. 3.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
4. 4.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 576 sq cm (c) 864 sq cm (d) 144 sq cm
5. 5.A cuboid is 9 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 258 sq cm (b) 129 sq cm (c) 270 sq cm (d) 516 sq cm
6. 6.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
7. 7.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 21 cu cm (d) 343 cu cm
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
10. 10.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
11. 11.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 2 times (d) 4 times
12. 12.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 150 sq cm (d) 125 sq cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
14. 14.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 204 sq cm (b) 102 sq cm (c) 51 sq cm (d) 54 sq cm
15. 15.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
16. 16.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
17. 17.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) 5 times (d) 8 times
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
19. 19.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
20. 20.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
21. 21.A cuboid is 5 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 130 cu cm (b) 14 cu cm (c) 20 cu cm (d) 100 cu cm
22. 22.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) 16 times (c) 4 times (d) 64 times
23. 23.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
24. 24.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 24 cu cm (d) 8 cu cm
25. 25.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 400 cu cm (d) 30 cu cm
26. 26.A cuboid is 8 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 416 sq cm (b) 192 sq cm (c) 208 sq cm (d) 104 sq cm
27. 27.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
28. 28.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
29. 29.A cuboid is 11 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 44 cu cm (b) 15 cu cm (c) 96 cu cm (d) 22 cu cm
30. 30.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
31. 31.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
32. 32.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
33. 33.A cuboid is 8 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 112 sq cm (b) 64 sq cm (c) 56 sq cm (d) 224 sq cm
34. 34.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
35. 35.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
36. 36.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
37. 37.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
38. 38.A cuboid is 12 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 213 sq cm (b) 540 sq cm (c) 426 sq cm (d) 852 sq cm
39. 39.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 8 sq cm (d) 24 sq cm
40. 40.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 95 sq cm (b) 126 sq cm (c) 190 sq cm (d) 380 sq cm

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