   Chapter 9.4, Problem 50E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Derive a formula for the total surface area of the hollow-core sphere.(Note: Include both interior and exterior surface areas.) To determine

To find:

The formula for the total surface area of the hollow-core sphere.

Explanation

Approach:

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=4πr2, 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 is V=43πr3.

Concentric spheres have the same center but different radii.

Calculation:

Consider a hollow-core sphere.

Length of the radius of the inside sphere =r

Length of the radius of the outside sphere =R.

To find the total surface area of the hollow-core sphere, we calculate the surface area of both the concentric spheres and add them up.

Total surface area of hollow-core sphere =Surface area o

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