MATHEMATICS 6 POWERPOINT PRESENTATION QUARTER 3 WEEK 7

lesson for quarter 3 math 6

1. MATH Surface Area Of Solid/Space Figures QUARTER 3 WEEK 7 DAY 1

2. Let’s solve the puzzle. The teacher will let the students finish the puzzle. What image will be formed?

3. What are these things? What sample of shape are these ? What other sample of cylinder, cone, and sphere?

4. These space figures have 0 edges and 0 faces. Each has a curved surface. Cone – 1 flat surface Cylinder – 2 flat surface Sphere – 0 flat surface

5. Surface are of cylinder The number of square units that exactly cover a cylinder is it surface area. The top and bottom bases are circular region. Thus, Area of top = Are of the bottom = r 2

6. The lateral surface is a rectangle. Thus, Are of the rectangle = I x w = 2r x h, because l is the circumference of the flattened circular surface.   Therefore, the formula for the surface are of cylinder is: Surface area = area of top + area of bottom + area of the lateral surface   = r 2 + r 2 + 2rh

7. Let’s try: Solve the word problem. The diameter of the base of a cylinder is 12 cm. if the height of the curved surface is 14 cm, what is the surface are of the cylinder? Solve and Show solution:

8. Instruction: Calculate the surface area of each cylinder. Give your answer in terms of . 1. Diameter = 6 cm; height = 8 cm 2. Diameter = 8ft; height 12ft 3. Radius = 10yd; height 4yrd

9. Remember: A cylinder, cone, and sphere have no vertices and edges.

10. Instruction: Find the total surface area of each cylinder. Round each answer to the nearest whole number. (Let  = 3.14) 10mm 60mm

11. MATH Surface Area Of Solid/Space Figures QUARTER 3 WEEK 7 DAY 2

12. What are the distinct properties of cylinder, cones, and sphere? Find out by doing the following activities. Needed Materials: Actual sample of solid figures like party hats, traffic cones, ice cream cone, balls, cans of milk, scented candles, balloons, and mugs (any available sample of the objects identified)

13. Task: group similar figures. Describe each figures and write its description in the respective column. cylinder cone sphere            

14. What have you notice in the different shapes ? Could you give other sample objects of these shapes?

15. Surface Area of a Cone The total surface are of the cone is the sum of its base are and curved surface area.   Circular base: Area A 1 =r 2

16. The flattened surface has an area of  rs , where s is called the slant height. The slant height (s) is the hypotenuse of a right triangle; thus, s = √h 2 + r 2   A cone is generated by this right triangle as it is made to revolve with fixed vertex (v) at the top forming s circular base of the radius ( r ) r = radius of the circular base h = height of the cylinder s = slant height (hypotenuse of the right triangle)   Hence, the relationship of h, r, and s is given by s= √h 2 + r 2

17. When the curve surface is flattened, it will result in a figure that looks like a triangle. The height or distance from the vertex to any point on the base is s. The figure’s base has a length equal to the circumference of the cone’s circular base. Thus, the area of this curved surface may be derived as:   A 2 = ½ bh = ½ (r) (s) A 2 =  rs

18. Total Surface are of a cone = area of curved face + are of the base.   The area of the base is r2. The area of the curve surface is  rs . Therefore, the surface are of a cone =  r2 +  rs .

19. Let’s Try: Find the surface of area of a cone with radius of 5 units and a slant height of 6 units.

20. Refer to the ice cream illustration below.

21. 1. What is the lateral surface of the cone? a.) 157 cm2 b .) 156 cm2 c .) 155 cm2 d .) 158 cm2 2. What is the circumference of the base of cone? a.) 31.40 cm b .) 314 cm c .) 3140 cm d .) 3.14 cm 3. What is the area of the base of cone? a.) 7.85 cm2 b .) 708.5 cm2 c .) 78.50 cm2 d .) 785 cm 4. What is the surface area of cone? a.) 23.55 cm2 b .) 235.50 cm2 c .) 24.55 cm2 d .) 230.50 cm2 5. If I put 90 cm2 of the ice cream inside the ice cream cone, do you think can suit to the ice cream cone, why? Or why not? Show your solution

22. Remember: SURFACE AREA OF CONE 𝑆 . 𝐴 . = 4 𝜋𝑟 2  

23. Calculate the surface of each cone. Give your answer in terms of 𝜋 1. Radius = 4ft; slant height = 10ft 2. Diameter = 12 in; slant height = 8in 3. Radius = 8.4 yd ; slant height = 6yd.

24. MATH Surface Area Of Solid/Space Figures QUARTER 3 WEEK 7 DAY 3

25. Surface of a Sphere   The surface are of a sphere of radius r is given by: Surface are = 4r 2

26. Example: find the surface are of the sphere with radius of 5 units. Surface = 4r 2 = 4 x 3.14 x 52 = 4 x 3.14 x 25 = 314 sq. units Therefore, the surface of the sphere is 314 sq. units.

27. Refer to the illustration below . 1 . What is the name of this solid figure? Sphere 2. What is the circumference of this figure? 31.4cm 3. What is the radius of the sphere? 5cm 4. What is the diameter? 10cm 5. What is the area? 78.5cm 2

28. Refer to the illustration below . 1. What is the circumference of the figure? a.) 50.24cm b.) 51.24cm c.) 49.24cm d.) 52.24cm 2. What is twice the area of this figure? a.) 200.96 cm 2 b.) 201.96 cm 2 c.) 202.96 cm 2 d.) 199.96 cm 2 3. If the radius is 20cm, what is the circumference of the sphere? a.) 124.60 cm b.) 125.60 cm c.) 126.60 cm d.) 123.60 cm 4. For this sphere, the surface area is cm 2 5. ________________ in 2

29. Find the surface area of a spherical ball whose radius is 8 cm.

30. Remember: In solving for the surface area of the sphere on the left, we will be using the formula: 𝑆𝐴 = 4 𝜋𝑟 2

31. MATH Surface Area Of Solid/Space Figures QUARTER 3 WEEK 7 DAY 4

32. Group Activity: Instruction: each group will solve the following word problems.   Group 1 – A marble has a radius of 12 mm. What is its surface area?   Group 2 - A small high pressure cylinder used in factories has a radius of 2.5 inches and a height of 15 inches. What is its surface area?   Group 3 - Marina wants to make a conical birthday cap with 3 inches in radius and 6 inches in slant height as dimensions. How much paper is needed to

33. GROUP ACTIVITY

34. Analyze the following problems by identifying the shape of the object mentioned in the problem and giving the formula needed. The first one is done for you.

35. Choose the letter of the best answer. Write your answer on the space provided. ______ 1) The formula 𝑆𝐴 = 2 𝜋𝑟 ( 𝑟 + ℎ ) may be used to solve for the surface area of a _____. A) Cone B) Cube C) Cylinder D) Sphere ______ 2) Annie wants to know the surface area of table tennis ball that has a diameter of 40 mm. What formula would Annie use? A) 𝑆𝐴 = 4 𝜋𝑟 2 C) 𝑆𝐴 = 2 𝜋𝑟 ( 𝑟 + ℎ ) B) 𝑆𝐴 = 6 𝑠 2 D) 𝑆𝐴 = 𝜋𝑟 ( 𝑟 + 𝑙 )

36. ______ 3) Joshua wants to create a paper party hat that has a radius of 3 inches and a slant height of 5 inches. How much polka dot paper will be needed to create the hat? A) 75.36 sq. inches C) 78.51 sq. inches B) 77.63 sq. inches D) 79.96 sq. inches

37. MATH Catch Up Friday QUARTER 3 WEEK 7 DAY 5