5 5 Geometry of Solids Goal TLW identify

5. 5 Geometry of Solids Goal: TLW identify solids and find their volumes and surface areas.

Prism: two faces are parallel and same size and shape. Cube Cuboid Hexagonal Triangular

Pyramid: polygon base and triangular faces that meet at a common point (apex). Square base triangular base pentagonal base

Solids with at least one curved face. Cylinder Cone Sphere

Surface Area: sum of all the area of the faces. 5 cm 2. 5 cm 10 cm

Find surface area 8 cm 6 cm 5 cm

Find surface area All edges are equal and have length 6 cm.

Surface area and the curved face.

Find the surface area Diameter of base = 9 cm Height = 13 cm

Find surface area 13. 6 cm 21 cm

Find surface area Diameter = 1 m

Volume: amount of space it occupies • • Cubic units Length is the distance between the bases. length

Volume formulas •

Find volume 12 cm 3. 8 cm 8. 5 cm

Find the volume 2 x 1. 5 x d x x

Example •

Example •

Lengths of line joining vertices with vertices, vertices with midpoints and midpoints. • In the cuboid ABCDEFGH, AB = 12 cm, BE = 10 cm and BC = 4. 5 cm. • Calculate the length of G D H C – AE – AC – BG • Let M be the midpoint of CH and R be the midpoint of GH. • Calculate the distance from – M to R – M to A E A B

Sizes of angle between two lines and between lines and planes. A Perpendicular to A from q. B q

Example G H • D C F 4. 5 cm E 10 cm A 12 cm B

Example G H • D C F 4. 5 cm E 10 cm A 12 cm B

Example • In the square-based pyramid in the diagram all the edges are 10 cm long and M is the midpoint of BC. • Find the length of AM • Find the angle that AM makes with the base of the pyramid. A D C E M B

Assignment • Sides 1 -11 p. 277 -278 #1 and 2 surface area only • Slides 12 - 17 p. 278 #2 volume, 3, 4, 6 • Slides 18 -22 p. 278 #5, 7, 8