If a sphere of radius r is sliced by a plane whose distance from the centre of the sphere is d, then the sphere is divided into two pieces called segments of one base (see the first figure).
The corresponding surfaces are called spherical zones of one base.
(a) Determine the surface areas of the two spherical zones indicated in the figure.
(b) Determine the approximate area of the Arctic Ocean by assuming that it is approximately circular in shape, with center at the North Pole and “circumference” at
(c) A sphere of radius r is inscribed in the right circular cylinder of radius r. Two planes perpendicular to the central axis of the cylinder and a distance h apart cut off a spherical zone of two bases on the sphere (see the second figure). Show that the surface area of the spherical zone equals the surface area of the region that the two planes cut off on the cylinder.
(d) The Torrid Zone is the region on the surface of the earth that is between the Tropic of Cancer (
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Calculus (MindTap Course List)
- Refer to the plate shown in Figure 117 and determine the following distances. All dimensions are in inches. a. The horizontal center distance between the 0.265" diameter hole and the 0.150" diameter hole. b. The horizontal center distance between the 0.385" diameter hole and the 0.150" diameter hole. c. The distance between edge A and the center of the 0.725" diameter hole. d. The distance between edge B and the center of the 0.385" diameter hole. e. The distance between edge B and the center of the 0.562" diameter hole.arrow_forwardWhich lines or line segments or rays must be drawn or constructed in a triangle to locate its aincenter? bCircumcenter? corthocenter? dcentroid?arrow_forwardA flat is cut on a circular piece as shown. Determine the distance from the center of the circle to the flat, dimension x.arrow_forward
- The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.arrow_forwardaBecause point Q is their common center, these circles are known as _ circles. bIf RQ=3 and QV=5, find the length of chord TV which is also a tangent to the inner circle.arrow_forwardThe larger circle is inscribed in a square with sides of length 4cm. The smaller circle is tangent to the larger circle and to two sides of the square, as shown. Find the length of the radius of the smaller circle.arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL