To find the surface area of a sphere, you use the formula:
Surface Area=4πr2\text{Surface Area}=4\pi r^2Surface Area=4πr2
where rrr is the radius of the sphere. This formula gives the total area covering the outer surface of the sphere and is expressed in square units (e.g., square centimeters, square meters)
Steps to calculate the surface area:
- Determine the radius rrr of the sphere. If you are given the diameter ddd, you can find the radius by dividing the diameter by 2:
r=d2r=\frac{d}{2}r=2d
- Substitute the radius value into the formula :
Surface Area=4πr2\text{Surface Area}=4\pi r^2Surface Area=4πr2
- Calculate the value using π≈3.1416\pi \approx 3.1416π≈3.1416.
Example:
If the radius of a sphere is 8 cm, then its surface area is:
4×π×82=4×3.1416×64=804.25 cm24\times \pi \times 8^2=4\times 3.1416\times 64=804.25\text{ cm}^24×π×82=4×3.1416×64=804.25 cm2
Alternative forms:
- Using diameter ddd:
Surface Area=πd2\text{Surface Area}=\pi d^2Surface Area=πd2
(because r=d2r=\frac{d}{2}r=2d, so 4πr2=4π(d2)2=πd24\pi r^2=4\pi \left(\frac{d}{2}\right)^2=\pi d^24πr2=4π(2d)2=πd2)
- If you know the volume VVV of the sphere but not the radius, you can first find the radius from the volume formula:
V=43πr3 ⟹ r=(3V4π)1/3V=\frac{4}{3}\pi r^3\implies r=\left(\frac{3V}{4\pi}\right)^{1/3}V=34πr3⟹r=(4π3V)1/3
Then substitute rrr into the surface area formula
. This formula is fundamental in geometry and widely used in physics, engineering, and various sciences when dealing with spherical objects. Summary:
Given| Formula for Surface Area of Sphere
---|---
Radius rrr| 4πr24\pi r^24πr2
Diameter ddd| πd2\pi d^2πd2
Volume VVV| 4π(3V4π)2/34\pi \left(\frac{3V}{4\pi}\right)^{2/3}4π(4π3V)2/3
(via radius calculation)
This is how you find the surface area of a sphere efficiently and accurately
