Spherical cap - Alchetron, The Free Social Encyclopedia
Spherical cap - Alchetron, The Free Social Encyclopedia
Jun 25, 2018
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The accompanying figure shows a spherical cap of radius ρand height h cut from a sphere of radius r. Show that the volume V of the spherical cap can be expressed as a. V=(1)/(3) πh^2(3 r-h) b. V=(1)/(6) πh^2(3 ρ^2+h^2). | Numerade
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numerade.com
SOLVED:A spherical cap is the region of a sphere that lies above or below a given plane. a. Show that the volume of the spherical cap in the figure below is (1)/(6) πh(3 a^2 h^2). b. A spherical segment is the solid defined by intersecting a sphere with two parallel planes. If the distance between the planes is h, show that the volume of the spherical segment in the figure below is (1)/(6) πh(3 a^2 3 b^2 h^2).
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numerade.com
SOLVED:The surface area of a spherical cap is given by S=2 πr h, where r is the radius of the sphere and h is the perpendicular distance from the sphere's surface to the plane intersecting the sphere, forming the cap. The volume of the cap is V=(1)/(3) πh^2(3 r-h). Similar to Exercise 61 , a formula can be found that will minimize the area of a cap that holds a specified volume. a. Solve the volume formula for the variable r. b. Substitute the resulting expression for r into the surface area for
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