Chapter 2.3

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Chapter 2.3

  1. 1. 22..33Area of a SphereWhat are you going tolearn?to state the area of asphere.to calculate the areaof a sphere.to state the volume ofa sphere.to calculate thevolume of a sphere.Key Termsany kinds of fruits have sphere-like shapes, such asoranges, tomato, melons.MMFigure 2.11:• sphere• area of a sphere.• volume of a sphere.Mention other objects around you, which are spheres in shape. A volley ball and abasket ball are spheres in shape.Figure 2.12How do you find the surface area of a ball? Do these activities./ Student’s Book – Space Figures with Curved Surface44
  2. 2. Work in Groups.Instrument and material : a slice of a hemispherical plastic ball, a nailand a piece of string.Mini - LabHow to do it :Make a hemispherical slice of a ball and stick the nail at the centre of thesurface like the following pictures.(a) (b)Arrange the string as Figure (a) till it covers the entire surface. Measure thatthe length of the string, say the length is x. Next, arrange the string on thehemispherical surface of the ball till it covers the entire surface, as shown inFigure (b). Measure the string length needed, say y.Compare the lengths of strings y and x. Is it true that the ratio is y : x = 2 : 1?or the ratio of y and x approaches 2:1? If the ratio only approaches 2:1, thenround it off to the nearest integer, so that y : x = 2:1.Stated in an equation, y = 2x. To cover the whole surface of the ball, we need2y strings, so that the area of the sphere surface (L) is formulated asA = 2y = 2. 2x = 4x.Because x equals the area of a circle, then x = π r 2. So the area of a sphere(L) isA = 4 π r 2,with r = radius of a sphereFormula forthe Surface ofSphereMathematics for Junior High School Grade 9 / 45
  3. 3. A solid spherical object has a diametre of 4.2 cm. Find the surface area of theobject (π =722).Solution :The radius of the solid spherical object r is 2.1, so that the surface area ofthe objectA = 4π r 2A = 4722(2.1) 2A = 55.44So the surface area of the object is 55.44 cm2.What is the radius of the sphere when its area is 7874cm2 and π =722?/ Student’s Book – Space Figures with Curved Surface46
  4. 4. Volume of SphereHow do you find the volume of a sphere?Mini - LabMini - LabLook at Figure 1 which shows a hemispherical object with aradius of r and Figure 2 which shows a cone with a length of r and aheight of t. If this cone is filled entirely with water and then it is pouredinto the hemispherical object, then the hemispherical object canaccomodate precisely twice the volume of the cone. Try to do it.Figure (1). Figure (2).Volume of a hemispherical object = 2 × volume of a coneVolume of a sphere = 2 × 2 volume of a cone= 4 × volume of a cone= 4 ×31π r 2t=34π r 2.r, t = r.=34π r 3rrt= rSo the formula of the Volume of a sphere (V) isV = 34 πr3,With r = radius of sphereFormula for theVolume of aSphereMathematics for Junior High School Grade 9 / 47
  5. 5. Find the volume of a sphere with a radius of 10 cm and π = 3.14.SolutionThe radius of the sphere r is 10, so the volume of the sphereV =34 π r 3V =34 3.14 (10)3V =34 (3140) = 418632So the volume of the sphere is 4,18632cm3.The radius of a sphere is 3 cm. Find the volume and the surface area.Solution:V =34π r 3=34π × 3 3 =34π × 3 × 3 × 3= 36 πL = 4 π r2= 4π × 3 × 3 = 36πSo the volume is 36π cm3 and the surface area is 36π cm2Find the length of the radius of a sphere, in which the volume is 1.437 31cm3 andπ =722./ Student’s Book – Space Figures with Curved Surface48
  6. 6. 1. Find the volume and the area of each of the following spheres with π = 3.14.a). basket ball b). tennis ball c). golf ball3 mDiametre = 24 cm Diametre = 4 cm Diametre = 68 mm2. Find the volume and area of each of the following spheres in π.a.b.c.3. Find the radius of a sphere in which the volume is 288π cm3.4. Find the radius of a sphere in which its surface area is 616 m2 and π =722.ExampleA sphere has radius of 3 cm, find its volumeand area of its side!Solution:V =34π r 3=34π × 3 3=34π × 3 × 3 × 3= 36 πA = 4 π r2= 4π × 3 × 3 = 36πSo its volume is 36π cm3andthe area of its side is 36π cm25 m15 mMathematics for Junior High School Grade 9 / 49
  7. 7. 5. The earth has the shape of a sphere with a radiusof 6,400 km and 70% of its surface is water. Findthe area of the water surface (in km2).6. A sphere-like balloon has a radius of 3 cm. The balloon is inflated to reach aradius of 7 cm. Find the difference in volume between before and after it isinflated.7. A box is made to contain 12 tennis balls asshown in the figure on the right. If the radius ofeach ball is 4.6 cm, find the perimetre of thesmallest possible rectangle that will take theballs./ Student’s Book – Space Figures with Curved Surface50

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