Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 99 · 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 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
3. 3.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
4. 4.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) 8 times (c) 64 times (d) 4 times
5. 5.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) 5 times (c) 125 times (d) 10 times
6. 6.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
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
8. 8.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
9. 9.A cuboid is 10 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 276 cu cm (b) 70 cu cm (c) 21 cu cm (d) 280 cu cm
10. 10.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
11. 11.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 216 cu cm (d) 144 cu cm
12. 12.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
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
14. 14.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 217 sq cm (d) 216 sq cm
15. 15.A cuboid is 11 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 18 cu cm (b) 110 cu cm (c) 55 cu cm (d) 174 cu cm
16. 16.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 16 sq cm (c) 64 sq cm (d) 97 sq cm
17. 17.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
18. 18.A cuboid is 11 cm long, 9 cm wide and 4 cm high. What is its total surface area? (a) 396 sq cm (b) 179 sq cm (c) 358 sq cm (d) 716 sq cm
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
20. 20.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
21. 21.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
22. 22.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 62 sq cm (b) 72 sq cm (c) 124 sq cm (d) 248 sq cm
23. 23.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
24. 24.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) 2 times (c) 4 times (d) 6 times
25. 25.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 140 sq cm (b) 560 sq cm (c) 280 sq cm (d) 300 sq cm
26. 26.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) 64 times (c) 16 times (d) 4 times
27. 27.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) 25 times (c) 5 times (d) 10 times
28. 28.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
29. 29.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
30. 30.A cuboid is 7 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 11 cu cm (c) 64 cu cm (d) 28 cu cm
31. 31.A cuboid is 10 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 416 sq cm (b) 104 sq cm (c) 140 sq cm (d) 208 sq cm
32. 32.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
33. 33.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) 64 times (d) 16 times
34. 34.A cuboid is 12 cm long, 9 cm wide and 5 cm high. What is its total surface area? (a) 852 sq cm (b) 540 sq cm (c) 213 sq cm (d) 426 sq cm
35. 35.A cuboid is 12 cm long, 8 cm wide and 9 cm high. What is its total surface area? (a) 276 sq cm (b) 552 sq cm (c) 1104 sq cm (d) 864 sq cm
36. 36.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
37. 37.If the side of a square 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
38. 38.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) 3 times (d) 6 times
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
40. 40.A cuboid is 8 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 24 cu cm (b) 240 cu cm (c) 268 cu cm (d) 21 cu cm

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