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# Chapter 2.1

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### Chapter 2.1

1. 1. Figure 2.3Figure 2.2Figure 2.1Figure 2.422..11Total Surface AreaWhat are you going tolearn?to mention the elementsof a cylinder.to draw cylinder nets.to explain the formula ofthe area of a cylinder’ssurface.to calculate the area ofa cylinder’s surface.to explain the formula ofthe volume of a cylinder.to calculate the volumeof a cylinder.to calculate the height orradius of a cylinder if thevolume is given.Key Terms:Observe the pictures ofsome cans on the right .What are the shapes of thecans?A cylinder has two circularbases and a lateral face.• cylinder• area of a cylinder’ssurface• area of a cylinder’s base• volume of a cHere are the mathematical figures.ylinderABABIf we cut the cylinder along the bases and alongstraight line AB in Figure 2.3 and we spread it ona plane, we will get a net as in Figure 2.4.Mathematics for Junior High School Grade 9 / 33
2. 2. For a better understanding, take a canof milk or any can with a label. If youcut the label as in Figure 2.5 andspread it on a plane, you will get arectangular figure. The width of therectangle is equal to the the height ofthe can and the length is thecircumference of the base.Figure 2.5Now, how do we find the total surface area?Look at the net of the cylinder below. The total surface area can befound by adding all the three areas.Total surface area = lateral area + 2 base area= 2πrh + 2πr2If the total surface area is called T, we have the formulafor T:Area of topbase = πr2Area of bottombase = πr2Area of lateral face= 2πrhRememberπ is a numberindicating thecomparisonbetween a round ofone circle (say K)with its diameter(say d)π=dKThe approximatevalue of π is 722 or3.14.T = 2πrh + 2πr2,where r = radius of cylinderh = heightFormula forthe TotalSurface Area34/ Student’s Book – Space Figures with Curved Surface
3. 3. Find the smallest area of an alluminum sheet formaking a can like the picture below. (Use π =722 )7 cm11.5 cmVolume of a CylinderWhat is the volume of a cylinder? We can use the formula of the volumeof a prism.(a) (b) (c)Figure 2.6The volumes of regular prisms (a) and (b) are the base area (A) times theheight (h). If the number of the sides increases to infinity, then the basewill be a circle. So, the volume of the cylinder is:V = A × hV = (π r2 ) × hV = π r2h,with r = radius of cylinderh = height of cylinderFormula for theVolume of aCylinderMathematics for Junior High School Grade 9 / 35
4. 4. Real life SituationIn many birthday parties, we often serve abirthday cake like the picture the on the left.Mostly, the cake of this kind is circular inshape. The diameter of the cake is 10 cm andthe height is 5 cm. Find the volume of thecake.To celebrate his birthday Arry serves herguests a two-layer cake as seen on thepicture on the left. The height of each layer is7 cm.If the diameter of the bottom cake is 30 cmand the diamater of the top one is 25 cm, findthe difference in volume of both layers.1. Determine the total surface area and the volume of each of the followingcylinders.a) b) c)7 cm10 cm15 cm14 cm7 cm12 cm36/ Student’s Book – Space Figures with Curved Surface
5. 5. 2. The front side of a heavy machine is a cylindrical inshape. The diameter of this part is 6 feet (foot/feet =feet contracted into ft) and the length is 8 feet. Howwide is the surface of the cylinder? What is thevolume of the cylinder?3. Someone wants to make a cylinder with the volume of 600 cm3. If theradius of the base of the cylinder is 5 cm, what is the height of the cylinder?4. If the volume of a cylinder is 135 π cm3 and the height is 15 cm, what is theradius of the cylinder?5. An oil refinery whose height is 32 m and whose diameter of the base side is 84 mwill be painted. What is the area of the refinery to bepainted? If one gallon of paint can be used to paint anarea of 325 m3, how many gallons of paint arerequired?6. The radius of a cylindrical tank is enlarged so that its radius is twice largerthan before. Find how much larger is its volume after being enlarged.7. The surface of a swimming pool has a circle in shape with circumference of77 meters. Calculate how much water is needed to fill in the pool if theheight is 1.2 meters.Mathematics for Junior High School Grade 9 / 37