Chapter 2.2

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Chapter 2.2

  1. 1. What you will learn:To state the area of acone side.To calculate the area ofa cone side.To state the volume of acone.To calculate the volumeof a cone.Key Terms:•••••ConeArea of a cone sideCone blanketVolume of a coneHeight of a coneWhat are you going tolearn?to state the area of acone surface.to calculate the area ofa cone surface.to state the volume of acone.to calculate the volumeof a cone.Key Terms:•••••conearea of a cone surfacecone blanketvolume of a coneheight of a cone22..22Surface Area of a ConeLLook at the picture of a farmer cap below.Figure 2.7The farmer’s cap is cone in shape.Figure 2.8 shows a cone and its parts.A cone has two parts, namely the baseand the lateral.stFigure 2.8On Figure 2.8 t is the height of the cone, r is the radius of the base, and s is theslant height.If the cone is cut along the slant s and its base, we will get the cone net which consistsof sector which has radius s and a circle with radius r, as shown by Figure 2.9.38 / Student’s Book - Space Figures with Curved Surface
  2. 2. BaseCircumference= 2πrL = area of sector(Lateral area)sABFigure 2.9Area of sector circumference of baseArea of circle circumference of big circle=Area of sectorsrππ22=The area of a cone surface(L) equals the sum of thearea of the sector plus thearea of base. So the totalsurface area is T = L + BArea of sector =srs2πArea of sector = π srArea of sector = π rsT = L + BT = π r (s + r)with r = radius of cone and s=slant heightTotalSurfaceAreaFind the area of the following cone.39 cm14 cmMathematics for Junior High School Grade 9 / 39
  3. 3. Solution:The radius of the base = ( r ) is 7 and the length of the slant height is 39, sothatT = π r (r + s)T =7227 (7 + 39)T = 22 (46) = 1012Therefore, the total area of the cone is 1.012 cm2.Volume of a ConeHow do you find the volume of a cone?Observe the following conesFigure 2.10The formula of the volume of a pyramid is V = 31Bt. Because the cone base is acircle with radius r, then B = π r 2 , so the volume of the cone is:Volume ofa ConeV = 31BhV = 31π r 2 t,with r = radius of cone andt = height of cone40 / Student’s Book - Space Figures with Curved Surface
  4. 4. Work in pairs/groupsInstruments: Three (3) congruent cones made of plastic, acylinder whose height is the same as the height of thecone, and sand.* Fill all cones with sand until they are full. Pour the sand fromthe cones into the cylinder. What will happen?Mini - LabA certain cone has the radius of 3.5 cm, the height is 15 cm, and π =722.Find the volume of the cone.Solution:The radius of the base r is 3.5 and the height is 15, so thatV = 31π r 2 tV =31.722. (3.5) 2 . 15V = 11. (3.5). 5 = 192.5So the volume of the cone is 192.5 cm3.Mathematics for Junior High School Grade 9 / 41
  5. 5. A volume of a cone is 462 cm3, the height of the cone is 9 cm, and π=722. Find the radius of the base.A teacher assigns two of his students to make cones as tall as 10 cm. Alimakes a cone with radius of 4 cm. Lia makes a cone with radius of 5 cm.What is the volume of Ali’s cone? What is the volume of Lia’s cone?1. Find the volume and the total surface area of each of the following cones. (π = 3.14)a. b. c.2. The radius of a cone base is 7 cm and the slant height is 13 cm.Find :a. the height of the coneb. the volume of the conec. the total surface area3. Mutia is going to have a birtdhday party. She willmake a party hat in conical figure as shown in thepicture on the left. If the height of the hat is 16 cmand the radius is 12 cm, how wide is the paperneeded for one hat?42 / Student’s Book - Space Figures with Curved Surface
  6. 6. 4. The volume of a cone is 1256 cm3. If the height of the cone is 12 cm, then find thelength of the cone radius (π = 3.14).5. The base radius of a cone is 3.5 m, the volume of the cone is 115.5 m3, the valueof π =722. Find the height of the cone.6. Critical Thinking A cone with a radius of 3 cm and a heightof 10 cm has the volume of 30π cm3.a. What is the volume if the radius is twice as much as theprevious radius?b. What is the volume of the cone now if the height is twiceas much as before?c. What is the volume of the cone if the height and radius aretwice as much as before?7. Find the radius (x ) of this cone if its volume is 21π.Mathematics for Junior High School Grade 9 / 43

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