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# Mathematics – sphere and prism

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### Mathematics – sphere and prism

1. 1. MATHEMATICS – SPHERE AND PRISM MUHAMMAD NAZMI YEE JYH LIN ERIK ONG ISYRAQ NASIR CHANG MAYCHEN RIFAI NUSAIR
2. 2. SPHERE
3. 3. WHAT IS A SPHERE?  A sphere is a geometrical figure that is perfectly round, 3- dimensional and circular - like a ball.
4. 4. WHAT IS A SPHERE?  Geometrically, a sphere is defined as the set of all points equidistant from a single point in space.  It is a shape of biggest volume with the smallest surface area.
5. 5. SPHEROID?  Watermelon and Earth is not exactly a sphere as it is not perfectly round. This are known as spheroid.
6. 6. PROPERTY OF A SPHERE  It is perfectly symmetrical  All points on the surface are the same distance from the center.  It has no edges or vertices (corners)
7. 7. SPHERE VOLUME AND SURFACE AREA
8. 8. VOLUME OF SPHERE  Volume= 4 3 𝜋𝑟3  General Formula for Volume of sphere  R is radius  By rearranging the above formula, you can find the radius:  Radius= 3 3𝑣 4𝜋
9. 9. EXAMPLE  Find the volume of a sphere of radius 9.6 m, rounding your answer to two decimal places.  V = 4 3 𝜋𝑟3  4 3 × 𝜋 × 9.63 (replace r with 9.6)  4 3 × 𝜋 × 884.736  = 3705.97 𝑚3 9.6 m
10. 10. SURFACE AREA OF SPHERE  Surface Area = 4𝜋𝑟2  By rearranging the above formula, you can find the radius:  Radius= 𝑎 4𝜋
11. 11. EXAMPLE  Find the surface area of a sphere of diameter 28 cm.  Radius = ½ Diameter  Surface Area = 4𝜋𝑟2  4 × 𝜋 × 142 (28 divide by 2 and replace r with it)  = 2464 𝑐𝑚2 28 m
12. 12. SUMMARY
13. 13. HEMISPHERE VOLUME AND SURFACE AREA
14. 14. VOLUME OF HEMISPHERE  It is exactly half of the sphere so:  4 3 𝜋𝑟3 ÷ 2  Volume = 2 3 𝜋𝑟3
15. 15. EXAMPLE  Find the volume of a hemisphere, whose radius is 10 cm.  V = 2 3 𝜋𝑟3  2 3 × 𝜋 × 103 (replace r with 10)  2 3 × 𝜋 × 1000  = 2093.3 𝑚3 10 cm
16. 16. SURFACE AREA OF HEMISPHERE  The surface area of hemisphere is equals to half of surface area of sphere plus the area of the base (circle).  2𝜋𝑟2 + 𝜋𝑟2  Therefore Surface Area =3𝜋𝑟2 this is only if the question asked about total surface area.
17. 17. EXAMPLE  Find the total surface area of a hemisphere, whose radius is 8 cm.  Surface Area = 3𝜋𝑟2  3 × 𝜋 × 82 (replace r with 10)  2 3 × 𝜋 × 64  = 602.88 𝑐𝑚2 10 cm
18. 18. PRISM
19. 19. WHAT IS A PRISM?  A prism is a geometrical solid object with two identical ends and flat sides.
20. 20. CROSS SECTION  A cross section is the shape made by cutting straight across an object.  A prism must have the same cross section all along its length.
21. 21. NO CURVES!  A prism is a polyhedron which means all faces must be flat.
22. 22. PARALLEL SIDES  The side faces of a prism are parallelograms.  When to ends are not parallel it is not a prism.
23. 23. PRISM VOLUME AND SURFACE AREA
24. 24. VOLUME OF PRISM  Volume = Base Area × Length  Base Area is calculated normally depends on the shape.
25. 25. EXAMPLE  What is the volume of a prism where the base area is 25 m2 and which is 12 m long:  Volume = Base Area × Length  𝑉𝑜𝑙𝑢𝑚𝑒 = 25 𝑥 12  = 300 𝑚3
26. 26. SURFACE AREA OF PRISM  Surface Area = (2 x Base Area) + (Base Perimeter x Length)
27. 27. EXAMPLE  What is the surface area of a prism where the base area is 25 m2, the base perimeter is 24 m, and the length is 12 m:  Surface Area = (2 x Base Area) + (Base Perimeter x Length)  𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = (2 × 25) + (24 × 12)  𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 50 𝑚2 + 288 𝑚2  = 338 𝑚2
28. 28. QUESTION!!
29. 29. Find the total surface area of a large round bowl (hollow hemisphere) with outer radius of 12 cm and thickness of 1 cm.
30. 30. ANSWER Outer Hemisphere: S.A = 2𝜋𝑟2 S.A = 2 × 𝜋 × 122 S.A = 2 × 𝜋 × 144 S.A = 288𝜋 Inner Hemisphere: S.A = 2𝜋𝑟2 S.A = 2 × 𝜋 × 112 S.A = 2 × 𝜋 × 121 S.A = 242𝜋 The ‘Ring’: S.A = 𝐵𝑖𝑔𝑔𝑒𝑟 𝑐𝑖𝑟𝑐𝑙𝑒 − 𝑆𝑚𝑎𝑙𝑙𝑒𝑟 𝑐𝑖𝑟𝑐𝑙𝑒 S.A = (𝜋 × 122) − (𝜋 × 112) S.A = 144𝜋 − 121𝜋 S.A = 23𝜋 Add All: 242𝜋 + 288𝜋 + 23𝜋 = 553𝜋 ≈ 𝟏𝟕𝟑𝟕. 𝟑 𝒄𝒎 𝟐
31. 31. Thank You
32. 32. REFERENCE http://www.calculatorsoup.com/calculators/geometry-solids/hemisphere.php http://www.rkm.com.au/CALCULATORS/calculator-images/MATHS-SPHERE-CIRCLE-equations-white- 500.png http://www.ditutor.com/solid_gometry/volume_hemisphere.html http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/nicholas4.html https://www.mathsisfun.com/geometry/prisms.html