Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 312 · 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 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 600 cu cm (d) 400 cu cm
2. 2.A cuboid is 8 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 144 sq cm (b) 360 sq cm (c) 180 sq cm (d) 90 sq cm
3. 3.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) 3 times (d) 9 times
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
5. 5.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 294 sq cm (d) 343 sq 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) 154 cm (d) 22 cm
7. 7.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
8. 8.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
9. 9.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 36 cu cm (d) 576 cu cm
10. 10.A cuboid is 8 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 208 cu cm (b) 192 cu cm (c) 32 cu cm (d) 18 cu cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
14. 14.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
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
17. 17.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 8 times (d) 2 times
18. 18.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
19. 19.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
20. 20.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
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
22. 22.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
23. 23.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
24. 24.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
25. 25.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 343 cu cm (d) 294 cu cm
26. 26.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
27. 27.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 15 cu cm (c) 125 cu cm (d) 150 cu cm
28. 28.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 10 cu cm (b) 60 cu cm (c) 104 cu cm (d) 13 cu cm
29. 29.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 24 cu cm (d) 6 cu cm
30. 30.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) 5 times (d) 25 times
31. 31.A cuboid is 10 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 19 cu cm (b) 50 cu cm (c) 200 cu cm (d) 220 cu cm
32. 32.A cuboid is 11 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 304 cu cm (b) 22 cu cm (c) 23 cu cm (d) 220 cu cm
33. 33.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 380 sq cm (b) 95 sq cm (c) 190 sq cm (d) 126 sq cm
34. 34.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
35. 35.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 180 sq cm (b) 45 sq cm (c) 90 sq cm (d) 50 sq cm
36. 36.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 30 sq cm (b) 31 sq cm (c) 124 sq cm (d) 62 sq cm
37. 37.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) 9 times (d) 27 times
38. 38.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
39. 39.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 64 sq cm (c) 256 sq cm (d) 384 sq cm
40. 40.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 24 cu cm (d) 512 cu cm

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