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# Surface area

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### Surface area

1. 1. by Maria Gloria G. Gabunada BSEd – Math 4 2011 – 2012
2. 2. What is a ?
3. 3. What is a ?Is the sum of the areas of all the faces of a solid.
4. 4. What is a ? The unit for surface area is expressed in square units.
5. 5. Recall:• A rectangular prism is a solid (3-dimensional) object which has six faces that are rectangles.• Area of a rectangular prism is given by the formula: – A = LW
6. 6. Length (L) Width (W) A1 = LW H A2 = L H Height (H)W A3 = LW W A4 = L H L
7. 7. To get the surface area of a rectangular Length (L) prism (SAr): Width (W) SAr = A1 + A2 + A3 + A4 + A5 + A6 A1 = LW H A2 = L H Height (H)W A3 = LW W A4 = L H L
8. 8. To get the surface area of a rectangular Length (L) prism (SAr): Width (W) SAr = A1 + A2 + A3 + A4 + A5 + A6 A1 = LW Note: A1 = A3 ; A2 = A4 ; A5 = A6 H A2 = L H Height (H) SAr = 2A1 + 2A2 + 2A5W A3 = LW W A4 = L H L
9. 9. To get the surface area of a rectangular Length (L) prism (SAr): Width (W) SAr = A1 + A2 + A3 + A4 + A5 + A6 A1 = LW Note: A1 = A3 ; A2 = A4 ; A5 = A6 H A2 = L H Height (H) SAr = 2A1 + 2A2 + 2A5W A3 = LW W By substitution, we get A4 = L H L
10. 10. Example #1:• Find the surface area of a rectangular prism whose length measures 7cm., width which measures 4cm. , and height which measures 2.5cm.
11. 11. Example #1: • Find the surface area of a rectangular prism whose length measuresH = 2.5cm 7cm., width which measures 4cm. , and height which measures 2.5cm.
12. 12. Example #1: H = 2.5cm• Find the surface area of a rectangular prism whose length measures 7cm., width which measures 4cm. , and height which measures 2.5cm.
13. 13. Solution #1: H = 2.5cm SAr = 2LW +2WH + 2LH SAr = 2(7cm)(4cm) + 2(4cm)(2.5cm) + 2(7cm)(2.5cm)Example #1:• Find the surface area of a SAr= 56cm2 + 20cm2 + 35cm2 rectangular prism whose length measures 7cm., width which measures 4cm. , and height SAr = 111 cm2 which measures 2.5cm.
14. 14. Recall: • a cube is a three- dimensional solid object bounded by six square faces. • Area of a square is given by the formula: – A = S2
15. 15. To get the surface area of a cube Sac: As = S2 SAs = S2 + S2 + S2 + S2 + S2 + S2 As = S 2 As = S 2 As = S 2 As = S 2 As = S 2
16. 16. To get the surface area of a cube Sac: As = S2 SAs = S2 + S2 + S2 + S2 + S2 + S2 As = S 2 As = S 2 As = S 2By simplifying, we get As = S 2 As = S 2
17. 17. Example #2:• find the surface area of a cube whose sides measure 3in.
18. 18. Example #2:• find the surface area of a cube whose sides measure 3in. S = 3inches
19. 19. Example #2:• find the surface area of a cube whose sides measure 3in.Solution #2: S = 3inchesSA s = 6S2SA s = 6(3in)2SA s = 54in2
20. 20. Notice: • It has a flat base and a flat top • The base is the same as the top, and also in- between • Because it has a curved surface it is not a polyhedron.
21. 21. • When we cut the body of a cylinder, we obtain a rectangle. – The formula for the area of a Ac =πr2 rectangle (Ar) is LxW • A right circular cylinder has 2 circular bases.Ar = 2πrh – The formula for the area of a circle (Ac) is πr2 • The length of the body of the Ac =πr2 cylinder is equal to the circumference of its circular bases. – L = 2πr – W = h (for height) • Ar = 2πrh
22. 22. To get the surface area of a right circular cylinder SA c = 2Ac + Ar Ac =πr2 SA c = 2πr2 + LW SA c = 2πr2 + 2πrhAr = 2πrh Ac =πr2
23. 23. To get the surface area of a right circular cylinder SA c = 2Ac + Ar Ac =πr2 SA c = 2πr2 + LW SA c = 2πr2 + 2πrhAr = 2πrh By simplification, we obtain Ac =πr2
24. 24. Example #3:• find the surface area of a right circular cylinder with a radius of 1.5 inches and a height of 5.2 inches.
25. 25. Example #3: • find the surface area of ar = 1.5in. right circular cylinder with a radius of 1.5 inches and a height of 5.2 inches. h = 5.2in.
26. 26. Example #3: • find the surface area of ar = 1.5in. right circular cylinder with a radius of 1.5 inches and a height of 5.2 inches. h = 5.2in. Solution #3: SA = 2π(r + h) SA s = 2π(1.5in.)(1.5in.+ 5.2in.) SA s = 3πin.(6.7in.) SA s = 201πin2
27. 27. • Units count. Use the same units for all measurements.• Surface Area of any prism is given by: Lateral area + Area of two ends