[PDF] [PDF] Chapter 19 Mensuration of Sphere - PBTE





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[PDF] Chapter 19 Mensuration of Sphere - PBTE

Applied Math Mensuration of Sphere Chapter 19 Mensuration of Sphere 19 1 Sphere: A sphere is a solid bounded by a closed surface every point of



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Applied Math Mensuration of Sphere Chapter 19

Mensuration of Sphere

19.1 Sphere:

A sphere is a solid bounded by a closed surface every point of which is equidistant from a fixed point called the centre. Most familiar examples of a sphere are baseball, tennis ball, bowling, and so forth. Terms such as radius, diameter, chord, and so forth, as applied to the sphere are defined in the same sense as for the circle. Thus, a radius of a sphere is a straight line segment connecting its centre with any point on the sphere. Obviously, all radii of the same sphere are equal. Diameter of the sphere is a straight line drawn from the surface and after passing through the centre ending at the surface. The sphere may also be considered as generated by the complete rotation of a semicircle about a diameter.

Great and Small Circles:

Every section made by a plane passed through a sphere is a circle. If the plane passes through the centre of a sphere, the plane section is a great circle; otherwise, the section is a small circle (Fig. 2). Clearly any plane through the centre of the sphere contains a diameter. Hence all great circles of a sphere are equals have for their common centre, the centre of the sphere and have for their radius, the radius of the sphere.

Hemi-Sphere:

A great circle bisects the surface of a sphere. One of the two equal parts into which the sphere is divided by a great circle is called a hemi- sphere.

19.2 Surface Area and Volume of a Sphere:

If r is the radius and d is the diameter of a great circle, then (i) Surface area of a sphere = 4 times the area of its great circle 369

Applied Math Mensuration of Sphere = 24ʌ

= 2ʌ (ii) Volume of a sphere =

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