L3 Mathematics Space Shape and Orientation

Itemoheleng campus Mathematics: Level 3 Shape, Space and Orientation Compiled by: Mrs. L Molaba…April 2020 Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume 1. Pyramids There are commonly four kinds of pyramids: a. Square Pyramid c. Triangular pyramid b. Rectangular Pyramid d. Hexagonal pyramid Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume Volume of a rectangular 𝟏𝟏 A = aln 𝟏𝟏 𝟐𝟐 pyramid: V = (area of base) 𝟑𝟑 Total area of a pyramid: × height Slant surface area + area Slant surface area of a of base pyramid: Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume Example: 1 1 V = (area of base) × h 3 1 = ×10×5×7 3 = 117 𝒎𝒎𝟑𝟑 Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume Example:2 Given: a= 30cm, v.height =20cm, n = 4 (square), l= ?, total area = ? a. Slant height = 𝑐𝑐 2 = 𝑎𝑎2 + 𝑏𝑏 2 = 152 + 202 = 625 = 25 cm Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume 𝟏𝟏 b. Slant surface area = aln 𝟐𝟐 𝟏𝟏 = (30)(25)(4) 𝟐𝟐 =1500 𝑐𝑐𝑐𝑐2 Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume 3. Area of base = 302 = 900 𝑐𝑐𝑐𝑐2 4. Total surface area = 1500 + 900 = 2 400 𝑐𝑐𝑐𝑐2 Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume 2. Pyramid Cone Area of a curved surface 2. The Cone Volume of a cone 𝟏𝟏 V = 𝜋𝜋𝑟𝑟 2 × h a. A = 𝜋𝜋𝒓𝒓𝒓𝒓 𝟑𝟑 Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume b. Area of base A = 𝜋𝜋𝑟𝑟 2 c. Total surface area= area curved surface + area of base Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume Example: 3 A solid sphere made of lead is to be melted and cast into conical shaped sinkers, to be used by fishermen. The sphere has a radius of 100 mm. The cone has a diameter of 60mm and vertical height is 50mm. Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume i . Determine the surface area of the sphere. A = 4𝜋𝜋𝑟𝑟 2 = 4𝜋𝜋(100)2 = 125 663.71 𝑚𝑚𝑚𝑚 2 Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume ii. Calculate the volume of the sphere 4 V(sphere) = 𝜋𝜋𝑟𝑟 3 3 4 = 𝜋𝜋(100)3 3 = 4188 790.2 𝑚𝑚𝑚𝑚 3 Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume iii. Determine the volume of the sinker 𝜋𝜋𝑟𝑟 2 ℎ V= =47 123.89 3 3 𝑚𝑚𝑚𝑚 𝜋𝜋 30 2 (50) = 3 Downloaded from hlayiso.com

Three-dimensional shapes: Calculating area and volume iv. Determine the number of sinkers that could be made 4188 790.2 =88.89 47 123.89 =88 sinkers could be made Downloaded from hlayiso.com

END OF SESSION 2 ENQUIRIES : −𝑏𝑏 ± 𝑏𝑏 2 − 4𝑎𝑎𝑎𝑎 2𝑎𝑎 INBOX THE LECTURER THANK YOU Downloaded from hlayiso.com