Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 140 · 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 11 cm. What is its total surface area? (a) 484 sq cm (b) 726 sq cm (c) 1331 sq cm (d) 121 sq cm
2. 2.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
3. 3.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 168 cu cm (b) 21 cu cm (c) 202 cu cm (d) 18 cu cm
4. 4.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 126 cu cm (b) 162 cu cm (c) 42 cu cm (d) 16 cu cm
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
7. 7.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 600 cu cm (c) 400 cu cm (d) 1000 cu cm
8. 8.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
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
11. 11.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
12. 12.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
13. 13.A cuboid is 11 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 174 cu cm (b) 22 cu cm (c) 110 cu cm (d) 18 cu cm
14. 14.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
15. 15.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
16. 16.A cuboid is 8 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 160 cu cm (b) 16 cu cm (c) 32 cu cm (d) 128 cu cm
17. 17.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) 25 times (c) 5 times (d) 10 times
18. 18.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) 6 times (d) 27 times
19. 19.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 27 cu cm (d) 54 cu cm
20. 20.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 150 cu cm (b) 18 cu cm (c) 190 cu cm (d) 15 cu cm
21. 21.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 50 sq cm (b) 200 sq cm (c) 56 sq cm (d) 100 sq cm
22. 22.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 484 cu cm
23. 23.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) 16 times (c) 4 times (d) 8 times
24. 24.A cuboid is 8 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 96 sq cm (b) 68 sq cm (c) 136 sq cm (d) 272 sq cm
25. 25.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
26. 26.A cuboid is 11 cm long, 9 cm wide and 9 cm high. What is its total surface area? (a) 891 sq cm (b) 1116 sq cm (c) 279 sq cm (d) 558 sq cm
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
28. 28.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 400 sq cm (c) 1000 sq cm (d) 600 sq cm
29. 29.A cuboid is 12 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 25 cu cm (b) 432 cu cm (c) 48 cu cm (d) 384 cu cm
30. 30.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
31. 31.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
32. 32.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
33. 33.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
35. 35.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
36. 36.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) 64 times (c) 16 times (d) 4 times
37. 37.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
38. 38.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
39. 39.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) 2 times (c) 4 times (d) 5 times
40. 40.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 100 cu cm (c) 15 cu cm (d) 150 cu cm

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