1. reas and Volume Areas and Volume

2. 2 Unit 4:Mathematics Aims Introduce standard formulae to solve surface areas and volumes of regular solids. Objectives Be able to use trigonometric methods and standard formula to determine areas and volumes.

3. Areas There is 2 types of areas  Cross Sectional Area  Surface Areas

4. Cross sectional Area PetryalSgwârCylch Triongl Paralelogram SectorAnnulus

5. Area of Regular Hexagon = A = * side 2 A = 2.598 x Side 2 (Approximately) If the side length of regular hexagon is 6 meter, calculate the area of regular hexagon using area formula? Given: Side length = 6 m. Area of Regular Hexagon = A = 2.598 x Side 2 A = 2.598 x 6 2 A = 2.598 x 36 A = 93.53 Therefore, Area of Regular Hexagon is 93.53 Square meter.

7. Area of parallelogram = 11 x 6 = 66cm² Radius of circle = 4 / 2 =2cm Area of circle = π x 2² =12.56637cm² Area of shape = 66 - 12.56637 =53.4cm²

8. Approximately how much aluminum is needed to cover this soda can that has a radius of 2 inches and a height of 5 inches? SA=2 π rh+2 π r 2 SA= 2(3.14)(2)(5)+2(3.14)(2)(2) SA= 62.8 +25.12 AA SA= 87.92 in. 2 of aluminum

10. Volume

12. The volume of every solid, liquid or gas, is how much three-dimensional space it occupies, often quantified numerically. Volumes of a number of simple shapes, such as regular, straight- edged, and circular shapes can be easily calculated using arithmetic formulas. More difficult shapes can be calculated by integral calculus if a formula exists for its boundary.

13. Rectangular prism Find the volume of the rectangular prism of sides 10cm, 15cm, 25cm. Let, a=10cm,b=15cm, c=25cm Formula used: a x b x c Solution: Volume of the rectangular prism = 10 x 15 x 25 = 3750 m 3

14. Sphere Volume of a sphere = 4/3πr 3 Find the volume of a sphere of radius 9.6 m Solution: Volume of a sphere = 4/3πr 3 = 4/3(3.14*9.6 3 ) = 1.33(3.14*884.736) = 1.33*2778.07104 = 3694.83 m 3

15. Cylinder Volume of a cylinder = πr 2 h Locate the volume of a cylindrical canister with radius 7 cm and height 12 cm. Solution: Volume of a cylinder = πr 2 h = 3.14* 7 2 *12 = 3.14*49*12 = 1846.32 cm 3

16. Triangular prism Find the volume of a triangular prism whose length is 3cm, base is 3cm and height is 3cm? Solution: Given: l = 3, b = 3, h = 3 Formula: Volume of a triangular prism = ½ (lb)h = ½ (3×3)3 = ½ (27) = 13.5cm 3

17. Square pyramid Volume of Square Pyramid = (1/3) b²h Locate the surface area and volume of a square pyramid with the given side 3, height 4 and the slant height 5. Solution: Volume of Pyramid = (1/3) b²h = (1/3)* 3² * 4 = 0.33 * 9 * 4 = 12.

18. Cone Volume = 1/3πr 2 h Locate the volume of cone whose base radius is 2.1 cm and height is 6cm using π =22/7 Solution: Volume = 1/3πr 2 h = 1/3*22/7* 2.1 2 *6 = 27.72 cm 3

19. Cube Volume = a³ Locate the volume, surface area and diagonal of a cube with the given side 3. Solution: Volume = a³ = 3³ = 27.

20. Area and volume of hexagon Volume of the hexagonal prism = cross sectional area (csa) x height(h). If the side length of regular hexagon is 8 cm and 3 meters high, calculate the area and volume of a regular hexagon?

21. Area and volume of hexagon Side length = 8 cm. Area of Regular Hexagon = A = (2.598) x Side 2 A = 2.598 x 8 2 A = 2.598 x 64 A = 166.27cm² Volume = csa x height = 166.27 x 300=49881cm³

22. How much paint will this paint can hold if it is 8 inches in diameter and 12 inches in height? V= π r 2 h V= 3.14(4)(4)(12) V= 602.88 in. 3 o baent of paint