हिन्दी में पढ़ेंHome › Formulas › 3D coordinates, lines & planes › Sphere
Sphere (3D coordinates, lines & planes)
(x − a)² + (y − b)² + (z − c)² = r²
Where: a = Sphere, b = b, c = y-intercept, r = radius, x = x, y = y, z = z
Solved example
Given: b = 7, c = 5, r = 10, x = 4, y = 3, z = 8
Find: a (Sphere)
- Formula: (-a + x)² + (-b + y)² + (-c + z)² = r²
- Rearranged for a: a = x + √(-b² + 2·b·y - c² + 2·c·z + r² - y² - z²)
- Substitute the values: a = 4 + √(10² - 3² + 2·3·7 - 5² + 2·5·8 - 7² - 8²)
- Rearranged for a: a = x - √(-b² + 2·b·y - c² + 2·c·z + r² - y² - z²)
- Substitute the values: a = 4 - √(10² - 3² + 2·3·7 - 5² + 2·5·8 - 7² - 8²)
- Result: a = 12.660254 ; a = -4.660254
Answer: a = 12.660254
Calculator
How to calculate Sphere (3D coordinates, lines & planes)
- Write down the formula: (x − a)² + (y − b)² + (z − c)² = r².
- Note the known values (b, c, r, x, y, z).
- Substitute them and simplify to find a.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Sphere (3D coordinates, lines & planes)?
The formula is (x − a)² + (y − b)² + (z − c)² = r², where a = Sphere, b = b, c = y-intercept, r = radius, x = x, y = y, z = z.
What is Sphere (3D coordinates, lines & planes) when b = 7, c = 5, r = 10, x = 4, y = 3, z = 8?
a = 12.660254. Substitute the values into (x − a)² + (y − b)² + (z − c)² = r² and simplify.