Concept explainers
Calculate the volume of a sphere that is circumscribed about the cube.
Answer to Problem 45HP
The volume of the sphere is
Explanation of Solution
Given:
It is given in the question that a cube has a volume of
Concept Used:
In this, use the concept of Pythagoras theorem, volume of cube and volume of sphere i.e.
Calculation: Here,
Since a circumscribed sphere will only intersect the cube at its vertices. The center of the sphere is the center of the cube.
CQ = QR= RP = 3 because they are half of the side of the cube. Using Pythagoras theorem, to find CR.
Again using the Pythagoras theorem to find CP , the radius of the
Now, the volume of the sphere is
Conclusion:
The volume is
Chapter 12 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
College Algebra
Essentials of Statistics (6th Edition)
A First Course in Probability (10th Edition)
Finite Mathematics & Its Applications (12th Edition)
Elementary Algebra
College Algebra (7th Edition)
- 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