Unit 14 - Volume (Word problems).pdf

Colegio Ntra. Seora del Prado (Ciudad Real) 1 ESO Volume

[1]

UNIT 14 VOLUME

1. POLYHEDRA

A. Key activities

1. Which of the following shapes are polyhedra and which are not? Explain why each of

the shapes is or is not a polyhedron.

a) Its a polyhedron because all its faces are flat

2. Some of the following shapes are prisms. Identify and describe each shape.

b) Its a rectangle-based prism or cuboid. Its bases and its lateral faces are

rectangles.

3. Explain why a cuboid is a prism.

A cuboid is a prism because its lateral faces are ___________ and it has two ___________ which are also rectangles.

4. Draw a prism whose base is a regular hexagon with all its parts. Draw its net too,

indicating also its parts.

5. Draw a pentagonal-based prism with all its parts. Draw its net too, indicating also its

parts.

6. Draw a pyramid whose base is a regular pentagon with all its parts. Draw its net too,

indicating also its parts.

7. Draw a hexagonal-based pyramid with all its parts. Draw its net too, indicating also

its parts.


[2]

8. Which of the following shapes are pyramids and which are not? Identify and describe

the shapes.

b) Its a square-based pyramid. Its base is a square. Its 4 lateral faces are

triangles that meet at a common vertex, called apex.

9. Study the following polyhedra and label the regular ones:

a) Its a regular polyhedron. Its four faces are equilateral triangles. Three faces

meet at each vertex.

10. Make a table describing the following polyhedra (what faces are, number of faces,

number of edges, number of vertices).

2. NON-POLYHEDRA

A. Key activities

11. Which of the following objects are solids of revolution? Name them.


[3]

12. Draw a cylinder with all its parts. Draw its net too, indicating also its parts.

13. Explain why the following nets do or do not belong to cylinders.

14. Draw a cone with all its parts. Draw its net too, indicating also its parts.

15. For each of the following cones, two of the three parts (radius, generatrix and

height) are known. Calculate the value of the unknown one.

16. Draw a sphere with all its parts. Draw its net too, indicating also its parts.

17. Using the words cylinder, cone and sphere describe the following solids.

18. For the following solids:


[4]

a) Which are polyhedra? Name the prisms and the pyramid.

b) Which are solids of revolution? Name them.

c) Is there anyone that its neither polyhedron nor solid of revolution?

3. VOLUME

A. Key activities

19. Find the volume of the 3D shape of the following figure

14 cm3

20. Find the volume of the following 3D shapes, taking one cube as the unit of volume

a) 8 cubes b) 27 cubes

21. Calculate the volume of the following figure when one cube is one dm3

33 dm3

22. Calculate the volume of the cuboid in the figure if dimensions are in cm. 18 cm

3


[5]

23. Calculate the volume of the following cuboids:

a) 4 dm, 2 dm and 7 dm 56 dm3

b) 0,5 dm, 25 cm and 1 dm 1,25 dm3

c) 0,07 m, 0,8 dm and 4,25 cm 0,238 dm3

d) 8 m, 80 dm and 800 cm 512000 dm3

24. Find the volume of the boxes of the figure:

a) 16 cm3 b) 18 m

3

25. Find the volume of the following polyhedra when dimensions are in cm.

a) 534,492 cm3 b) 12 cm

3

26. The base of a prism is a regular hexagon with side 7 cm and apothem 6,06 cm. Find

the volume of the prism knowing that its height is 10 cm. 1272,6 cm3

27. The area of the base of this prism is 226,16 cm2. Calculate its volume. 1809,28 cm

3

28. Find the volume of the following prism. 25 cm3


[6]

29. Find the volume of a pyramid whose base is a square with a side of 5 cm, being its

height the triple of the side of the base. 125 cm3

30. Calculate the volume of the pyramid in the figure. 40 cm3

31. The base of the pyramid in the figure is a square. Find its volume. 53,33 cm

3

32. Calculate the volume of a tower in Miguelturra whose base is a regular hexagon.

The apothem is 1,72 m while the side is 2 m. The height of the pyramid is 6 m 20,64 m3

33. Calculate the volume of the following cylinders when dimensions are in cm.

a) 197,82 cm3 b) 157 cm

3

34. Calculate the volume of the following cylinders:

a) h = 8 cm and r = 50 mm 628 cm3

b) h = 20 cm and r = 1 dm 6280 cm3

c) h = 2,5 dm and r = 15 cm 17662,5 cm3

35. To build the basement of a house a cylinder with a diameter of 6 m and a height of 5

m has been built. Calculate its volume. 141,3 m3


[7]

36. Calculate the volume of the following cylinders when dimensions are in cm.

a) 261,67 cm3 b) 50,24 cm

3

37. Calculate the volume of the following cones:

a) h = 0,5 dm and r = 1 cm 5,233 cm3

b) h = 20 cm and r = 1 dm 2093,333 cm3

38. The height of a cone-shaped tower is 3/5 of its diameter, being this 8 m. Find the

volume of the tower. 80,384 m3

39. Calculate the volume of the spheres in the figure, dimensions being in m.

a) 33,493 m3 b) 1259,194 m

3

40. The diameter of the official football ball for the next World Cup in Brazil is 22,3

cm. Find its volume in dm3. 5,8 dm

3

41. Calculate the volume of the sphere in the figure 113,973 cm3

42. Calculate the volume in cm

3 of the spheres whose radius is:

a) 1,1 cm 5,572 cm3 b) 1,5 dm 14130 cm

3 c) 0,05 m 523,33 cm

3

43. The diameter of a sphere is 0,5 m. Find its capacity in liters. 67,417 l


[8]

B. Excellence activities

44. The base if the pyramid in the figure is a rectangle, being one side twice the other

one. Find its volume. 72 cm3

45. The diameter of a cylinder-shaped glass is 4,5 cm while its height is 5 cm. How

many glasses can be filled out of a 1,5 liters bottle? 18 glasses

46. Find the amount of material used to build the 3D shape in the figure. 6280 cm3

47. Find the volume of a cone whose generatrix is 25 cm long and its diameter is 18 cm.

1977,069 cm3

48. En un recinto ferial se ha instalado una carpa, siendo la parte inferior cilndrica y la

superior cnica. El dimetro de la parte cilndrica mide 30 m y su altura 10 m. la altura

de la parte cnica es de 8 m. Cul es el volumen del circo? 8949m3

49. Have a look at the following figures and make an estimation about which one has a

bigger volume. Then check your estimation calculating its volumes.

Vc = 1 m3

Vs = 0,523 m3


[9]

50. The radius of the Earth is 6369 km and the radius of the Moon is 1738 km. How

many times is bigger the volume of the Earth? 49,2 times

51. En los siguientes envases Andrea ha decidido poner su capacidad y su volumen.

Para ello ha elaborado unas etiquetas que hay que pegar en el hueco en blanco que hay

en cada uno de ellos. Colcalas.

52. Las medidas de las siguientes figuras estn dadas en cm. Borja y Ariadna calcularon

su volumen en el folio que hay escrito al lado, pero ahora no saben cul corresponde a

cada una de ellas. Aydales y escribe debajo de cada figura su volumen

correspondiente.

Documents

Unit 14 - Volume (Word problems).pdf