118 Surface Areas and Volumes of Spheres
This is the formula for the surface area of a sphere chord of a sphere, p 648 great circle, p 648 Previous sphere center of a sphere radius of a sphere diameter of a sphere hemisphere Core VocabularyCore Vocabulary CCore ore CConceptoncept Surface Area of a Sphere The surface area S of a sphere is S = 4πr2 where r is the radius of the
Surface Area of a Sphere - MIT OpenCourseWare
surface area of a sphere gives us just such an answer We’ll think of our sphere as a surface of revolution formed by revolving a half circle of radius a about the x-axis We’ll be integrating with respect to x, and we’ll let the bounds on our integral be x 1 and x 2 with −a ≤ x 1 ≤ x 2 ≤ a as sketched in Figure 1 x1 x2
MAP PROJECTIONS: REPRESENTINGA SPHERICAL SURFACE ON A FLAT PLANE
1 Aitoff: The entire sphere fits onto an ellipse with 2:1 axial ratio 2 Mollweide: Much like the Aitoff The entire sphere fits onto an ellipse with 2:1 axial ratio 3 Sinusoidal: The horizontal length is the cosine of the distance from the equator, which makes the pixels equal area 4
On the mapping of Spherical Surfaces onto the Plane
point from the sphere is imaginary 2 In Figure 1, abcrepresents a portion of the Spherical surface, whose pole is at the point band Equator the circle alc Let abbe the prime Meridian, from which, as is usual in Geography, the longitude of a point on the Sphere is measured Now consider an arbitrary point p, which lies on the Meridian
Spheres Date Period
Find the surface area of each figure Round your answers to the nearest tenth, if necessary 1) 3 ft 2) 12 cm 3) 15 6 in 4) 7 cm 5) 8 in 6) 10 mi 7) A sphere with a diameter of 6 2 in 8) A sphere with a radius of 10 mi -1-
Gauss’ Law
sphere as the Gaussian surface The electric field is given by Since E is radial, its dot product with the differential area vector, which is also radial, is always one Also E is the same at every point on the surface of the sphere
Chapter 4 Gauss’s Law - MIT
the shape of the imaginary Gaussian surface we choose to enclose the charge qenc To prove Gauss’s law, we introduce the concept of the solid angle Let be an area element on the surface of a sphere of radius , as shown in Figure 4 2 4 11 ∆=Ar∆A ˆ r S1 r1 Figure 4 2 4 The area element ∆A subtends a solid angle∆Ω
Drag on Spheres
3 Observe the “drag crisis” associated with a sphere at high Reynolds numbers, and the effect of surface roughness on sphere drag 4 Measure the drag coefficient of a model car for several configurations, and compare Equipment 1 high speed undergraduate wind tunnel 2 Validyne electronic pressure transducer and digital manometer, Model
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