Suppose that a semicircular region with vertical diameter of length 4 is rotated about that diameter. Determine the exact surface area and the exact volume of the resulting solid of revolution.
The surface area and volume of the solid of revolution.
A solid of revolution is obtained by rotating a plane region around a straight line lying on the same plane. The straight line is called the axis of revolution. It may be vertical, horizontal or oblique.
A sphere is a three dimensional solid figure, which is made up of all the points in space, which lie at a common distance, called the radius, from a fixed point called the center of the sphere. The surface area of a sphere S = , where r is the radius of the sphere.
All solid bodies occupy space. The measure of occupied space is called the volume of the object. Volume of a sphere = V =.
Consider a semi circular region that is rotated about its vertical diameter. The resultant solid of revolution that is formed is a sphere, with diameter d = 4.
Radius r =
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Calculus: Early Transcendental Functions
Calculus: An Applied Approach (MindTap Course List)
Single Variable Calculus
Mathematical Applications for the Management, Life, and Social Sciences
Calculus: Early Transcendentals
Essentials Of Statistics
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus (MindTap Course List)
Elementary Technical Mathematics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Understanding Basic Statistics
Single Variable Calculus: Early Transcendentals, Volume I
Statistics for The Behavioral Sciences (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Mathematical Excursions (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Elements Of Modern Algebra
Single Variable Calculus: Early Transcendentals
Calculus of a Single Variable
Contemporary Mathematics for Business & Consumers
Trigonometry (MindTap Course List)
Finite Mathematics for the Managerial, Life, and Social Sciences
Calculus: Early Transcendental Functions (MindTap Course List)