Practice - Equation of a Sphere
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Practice Questions
Test your understanding with targeted questions
What is the equation of a sphere with center at (0, 0, 0) and radius 1?
💡 Hint: Use the simplest form of the sphere equation.
If a sphere has a center at (1, 1, 1) and radius 2, what is its equation?
💡 Hint: Plug the values of the center and radius into the standard equation.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the variable 'r' represent in the equation of a sphere?
💡 Hint: Think about what defines the size of the sphere.
True or False: The equation of a sphere can only be expressed when the center is at the origin.
💡 Hint: Consider different center points.
1 more question available
Challenge Problems
Push your limits with advanced challenges
If a sphere centered at (3, 2, -1) intersects the coordinate axes at certain points, what are these intersection points if the radius is 4?
💡 Hint: Use the center and radius to find how far the sphere extends from the center towards each axis.
Given the equation $(x + 4)^2 + (y - 3)^2 + (z + 7)^2 = 49$, identify the center and discuss how the sphere would visually appear in 3D space.
💡 Hint: Focus on the signs before each component in the equation as they correspond to the center's location.
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