Our Lady of the Rosary College. F. 3 Mathematics

Transcription

1 Our Lady of the Rosary ollege F. 3 Mathematics hapter 4 Study of Three imensional Figures lass: Name: ( )

2 F.3 Study of 3-figures P. 1 I. Review. Solids with uniform/non-uniform cross-sections Write down the names of the following solids. State whether they have uniform or non-uniform cross-sections. (1) (2) (3) (4) Solid Name of solid ross-section (5) (6) (7) (8) Solid Name of solid ross-section. Reflectional and Rotational Symmetry of Plane Figures In each of the following figures, draw and write down the number of axis/axes of reflectional symmetry using dotted line(s), and also write down the order of rotational symmetry. (1) (2) (3) (4) Figure No of axis/axes of reflectional symmetry Order of rotational symmetry

3 (5) (6) (7) (8) F.3 Study of 3-figures P. 2 Figure No of axis/axes of reflectional symmetry Order of rotational symmetry II. Symmetry of Solids. Reflectional Symmetrical Solids 1. raw 3 different planes of reflection of a cube. 2. raw 2 different planes of reflection of a regular tetrahedron. 3. raw a plane of reflection of the following solids with uniform cross-sections. (a) Regular hexagonal prism (b) ylinder (c) Regular triangular prism

4 F.3 Study of 3-figures P raw a plane of reflection of the following solids with non-uniform cross-sections. (a) Regular pentagonal pyramid (b) Regular octahedron (c) one (d) Sphere (e) Right trapezium-based pyramid (f) Right rectangular pyramid ssignment: lasswork 4.1. Rotational Symmetrical Solids 1. raw 3 different axes of rotation of a cube and write down the number of folds of rotational symmetry for each axis of rotation. 2. raw 2 different axes of rotation of a regular tetrahedron and write down the number of folds of rotational symmetry for each axis of rotation.

5 F.3 Study of 3-figures P raw an axis of rotation and write down the number of folds of rotational symmetry of the following solids with uniform cross-sections. (a) uboid (b) ylinder (c) Regular octagonal prism 4. raw an axis of rotation and write down the number of folds of rotational symmetry of the following solids with no uniform cross-sections. (a) Regular hexagonal pyramid (b) Hemisphere (c) one III. Nets of Solids When a hollow solid is cut along some of its edges, it can be folded to form a plane figure. This plane figure is called the net of the solid.. ube The nets of a hollow cube are shown below. raw 3 more different nets of a hollow cube.

6 . Triangular Prism raw 2 different nets of a hollow triangular prism. F.3 Study of 3-figures P. 5. Solids with uniform cross-sections raw any one net of the following solids. 1. ylinder 2. uboid 3. Regular pentagonal prism

7 . Solids with no uniform cross-sections raw any one net of the following solids. 1. Regular pentagonal pyramid F.3 Study of 3-figures P Regular octahedron 3. one ssignment: 1. lasswork x 4 (4, 5, 6, 9, 10, 12) (Q.5 and 12 are optional, Q.6: raw 1 net instead of 3)

8 F.3 Study of 3-figures P. 7 I. Projection of 3-imensional Figures. Review [The following solids are formed by cubes. The numbers in the figures shows their sizes.] 1. Using point as the lowest point, draw the following solids on the given isometric grids. 2. Using the shaded surface as the front surface, draw the following solids on the given oblique grids.

9 F.3 Study of 3-figures P. 8. Warm-up xercise (Group work) 12 small cubes are given. Try to make as many different solids as possible and draw its oblique, isometric and orthographic projection. State the number of cubes used. [For some solids, oblique projection cannot be shown. The number of cubes used must be greater than 6.] No. of cube used Oblique Projection Isometric Projection Orthographic Projection

10 F.3 Study of 3-figures P. 9 No. of cube used Oblique Projection Isometric Projection Orthographic Projection

11 F.3 Study of 3-figures P. 10. Orthographic Projections (From Solids to iews) 1. raw the orthographic projection (top view, side view and front view) of each of the a. following solids.[from oblique projection to orthographic projection] b. c. d. e.

12 2. raw the orthographic projection of each of the following solids. [From isometric projection to orthographic projection] a. F.3 Study of 3-figures P. 11 b. c. d. e. f. ssignment : lasswork 4.4, 4.6

13 F.3 Study of 3-figures P. 12. Oblique Projection (From iews to Solids) raw the oblique projection of each of the following solids according to its orthographic projection ssignment: lasswork 4.5

14 F.3 Study of 3-figures P. 13. Isometric Projection (From iews to Solids) raw the isometric projection of each the following solids according to its orthographic projection ssignment: lasswork 4.4

15 . Properties of Lines and Planes of Solids. Solids with No Uniform ross-section 1. Pyramids F.3 Study of 3-figures P. 14 M X Right rectangular pyramid Right triangular pyramid ertex Foot of perpendicular ase Height Slant edge Lateral face 2. ones O - O - O (right), (oblique) O O - Right circular cone Oblique cone 3. Spheres Some examples of spheres: O - O O -

16 . Perpendicular lines of a plane 1. (a) P is the projection of. (b) Is PP MP? (c) Is PP NP? (d) Is PP LP? (e) PP is to the plane. (f) Mark all the right angles in the figure. F.3 Study of 3-figures P. 15 P x L M P N 2. (a) raw the projection of point, indicate it as. (b) raw any 2 lines on the plane PQRS from so that is perpendicular to the plane PQRS. (c) Write down the 2 pairs of perpendicular lines and indicate the right angles in the figure. [Indicate all the right angles in the figure.] Q P x R S. ngle between a line and a plane Q 1. (a) PQ is the projection of. (b) is the angle between the line PQ and the plane. P Q 2. (a) raw the projection of, indicate it with and show the right angle in the figure. P S (b) is the angle between the line and the plane PQRS. Q R 3. is a rectangle and is a triangle. Mark the angle between and the plane. The angle is. 4. and are two triangles. Mark the angle between and the plane. The angle is.

17 . ngle between two planes 1. (a) The projection of M is. (b) The projection of MN is. (c) is the line of intersection of and PQRS. (d) PQ and NM. (e) is the angle between the plane and the plane PQRS. F.3 Study of 3-figures P. 16 S R M M P Q N 2. Y is a point on the plane PQRS. Through Y, draw and mark the angle between S Y x R the two planes and PQRS. The angle is. [Indicate all the right angles in the figure.] P Q 3. is a rectangle and is a triangle. Mark the angle between these two planes. The angle is. 4. and are isosceles triangles. Mark the angle between these two planes. The angle is. 5. is a rectangle and is a triangle. Mark the angle between these two planes. The angle is. ssignment: x 4

18 F.3 Study of 3-figures P. 17. xercise (Properties of lines and planes of solids) 1. The figure shows a right triangular prism. Mark all right T U S R angles at the vertices. P Q G H 2. In the figure, FGH is a cuboid. raw the line segment H and its projection on the plane FGH. Mark and name the angle between them. F 3. In the figure, is a right rectangular pyramid. raw the projection of the line segment on the plane. Mark and name the angle between them. K L J G I F H 4. The figure shows a right regular hexagonal prism. Mark and name the angle between the line segment I and the plane F. 5. In the figure, F is a right regular hexagonal pyramid. Mark and name the angle between the line segment and the base F. F 6. In the figure, is a regular tetrahedron. is the projection of on the plane. Mark and name the angle between the line segment and the plane. x

19 F.3 Study of 3-figures P. 18 H 7. The figure shows a cube. Mark and name the angle between the plane F and FGH. G F P 8. In the figure, FGH is a right prism. P is a point on. Mark and name the angle between the planes PH and FGH. F H G 9. The figure shows a cuboid. H a. Mark and name the angle between the planes and GH. G F b. Mark and name the angle between the planes and H. 10. The figure shows a pyramid with a quadrilateral base. a. Mark and name the angle between the planes and. b. Mark and name the angle between the planes and.

20 F. xercise (Properties of lines and planes of solid) 1. FGH is a rectangular prism and M is the intersection of and. F.3 Study of 3-figures P. 19 (a) Mark and name the angle between the line F and the plane (Figure 1a). (b) Mark and name the angle between the line F and the plane (Figure 1a). (c) Mark and name the angle between the line and the plane (Figure 1a). (d) Mark and name the angle between the planes and GF (Figure 1b). (e) Mark and name the angle between the planes and H (Figure 1b). (f) Mark and name the angle between the planes and F (Figure 1c). Figure 1a F Figure 1b F Figure 1c F H G H G H G M 2. is a rectangular pyramid. M is the intersection of and and N is a mid-point of. (a) Mark and name the angle between the line and the plane (Figure 2a). (b) Mark and name the angle between the line N and the plane (Figure 2a). (c) Mark and name the angle between the plane and the plane (Figure 2b). (d) Mark and name the angle between two planes and (Figure 2b). (e) Mark and name the angle between two planes and (Figure 2c). Figure 2a Figure 2b Figure 2c M N M N M N

21 3. is a triangular prism and is a right-angles triangle. (a) Mark and name the angle between the line and the plane. F.3 Study of 3-figures P. 20 (b) Mark and name the angle between the line F and the plane. (c) Mark and name the angle between the line F and the plane. (d) Mark and name the angle between the plane F and the plane. F 4. is a triangular pyramid. M is a mid-point of and X M. (a) Mark and name the angle between the line and the plane (Figure 4a). (b) Mark and name the angle between the line M and the plane (Figure 4b). (c) Mark and name the angle between the plane and the plane (Figure 4b). (d) Mark and name the angle between the plane and the plane (Figure 4c). Figure 4a Figure 4b Figure 4c X M X M X M

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