If a sphere of radius r is sliced by a plane whose distance from the center 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 75° north latitude. Use r = 3960 mi for the radius of the earth.
(c) A sphere of radius r is inscribed in a 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 (23.45° north latitude) and the Tropic of Capricorn (23.45° south latitude). What is the area of the Torrid Zone?
Trending nowThis is a popular solution!
Chapter 8 Solutions
Calculus: Early Transcendentals
- 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_forwardThe center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. 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_forwardDoes the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?arrow_forward
- Does a right circular cylinder such as an aluminum can have a symmetry with respect to at least one plane? b symmetry with respect to at least one line? c symmetry with respect to a point?arrow_forwardThe surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9 cm2 and area of each regular hexagon is 52.5 cm2. a What is the surface area of the soccer ball? b If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?arrow_forwardThree spheres are externally tangent to each other in pairs. Their radii have lengths of 1 in., 2 in., and 3in., respectively. What type of triangle is formed by the lines of centers?arrow_forward
- A flat is cut on a circular piece as shown. Determine the distance from the center of the circle to the flat, dimension x.arrow_forwardFor compactness, the drop-down wheels of a stretcher or gurney are folded under it as shown. In order for the boards upper surface to be parallel to the ground when the wheels are dropped, what relationship must exist between AB and CD?arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning