Sphere Surface Area Calculator
Calculate sphere surface area and volume from radius: SA = 4πr²
Enter Radius
Volume: 523.60 cubic units
Calculations:
Surface Area: SA = 4πr² = 4π(5)² = 4π(25) = 100π = 314.16 square units
Volume: V = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 523.60 cubic units
Sphere Surface Area Formula
Surface Area: SA = 4πr²
Volume: V = (4/3)πr³
where: - r = radius of the sphere - π ≈ 3.14159
How to Calculate Sphere Surface Area
- Measure the radius: Find the distance from the center to any point on the surface
- Square the radius: Calculate r² = r × r
- Multiply by 4: Calculate 4r²
- Multiply by π: Surface Area = 4πr²
Understanding Surface Area
The surface area of a sphere equals exactly four times the area of a great circle (a circle with the same radius as the sphere). This elegant relationship was first proven by Archimedes, who showed that the surface area of a sphere equals the lateral surface area of a cylinder that just encloses it.
Real-World Applications
Sphere surface area calculations are used in: - Painting and coating: Amount of paint needed for spherical objects - Manufacturing: Material needed for ball bearings and domes - Earth science: Calculating Earth's total surface area - Medicine: Drug dosage calculations based on body surface area approximations - Sports: Surface material requirements for balls
Common Questions
What is the formula for sphere surface area?
The sphere surface area formula is SA = 4πr², where r is the radius. This means the surface area is exactly four times the area of a circle with the same radius.
How do you find the radius of a sphere from its surface area?
To find the radius from surface area, use r = √(SA / 4π). Divide the surface area by 4π, then take the square root.