How to Find the Radius of a Sphere
Find the radius if you know the diameter., Find the radius if you know the circumference., Calculate the radius if you know the volume of a sphere., Find the radius from the surface area.
Step-by-Step Guide
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Step 1: Find the radius if you know the diameter.
The radius is half the diameter, so use the formula r = D/2.
This is identical to the method used for calculating the radius of a circle from its diameter.If you have a sphere with a diameter of 16 cm, find the radius by dividing 16/2 to get 8 cm.
If the diameter is 42, then the radius is
21. -
Step 2: Find the radius if you know the circumference.
Use the formula C/2π.
Since the circumference is equal to πD, which is equal to 2πr, dividing the circumference by 2π will give the radius.If you have a sphere with a circumference of 20 m, find the radius by dividing 20/2π =
3.183 m.
Use the same formula to convert between the radius and circumference of a circle. , Use the formula ((V/π)(3/4))1/3.The volume of a sphere is derived from the equation V = (4/3)πr3.
Solving for the r variable in this equation gets ((V/π)(3/4))1/3 = r, meaning that the radius of a sphere is equal to the volume divided by π, times 3/4, all taken to the 1/3 power (or the cube root.)If you have a sphere with a volume of 100 inches3, solve for the radius as follows: ((V/π)(3/4))1/3 = r ((100/π)(3/4))1/3 = r ((31.83)(3/4))1/3 = r (23.87)1/3 = r
2.88 in = r , Use the formula r = √(A/(4π)).
The surface area of a sphere is derived from the equation A = 4πr2.
Solving for the r variable yields √(A/(4π)) = r, meaning that the radius of a sphere is equal to the square root of the surface area divided by 4π.
You can also take (A/(4π)) to the 1/2 power for the same result.If you have a sphere with a surface area of 1,200 cm2, solve for the radius as follows: √(A/(4π)) = r √(1200/(4π)) = r √(300/(π)) = r √(95.49) = r
9.77 cm = r -
Step 3: Calculate the radius if you know the volume of a sphere.
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Step 4: Find the radius from the surface area.
Detailed Guide
The radius is half the diameter, so use the formula r = D/2.
This is identical to the method used for calculating the radius of a circle from its diameter.If you have a sphere with a diameter of 16 cm, find the radius by dividing 16/2 to get 8 cm.
If the diameter is 42, then the radius is
21.
Use the formula C/2π.
Since the circumference is equal to πD, which is equal to 2πr, dividing the circumference by 2π will give the radius.If you have a sphere with a circumference of 20 m, find the radius by dividing 20/2π =
3.183 m.
Use the same formula to convert between the radius and circumference of a circle. , Use the formula ((V/π)(3/4))1/3.The volume of a sphere is derived from the equation V = (4/3)πr3.
Solving for the r variable in this equation gets ((V/π)(3/4))1/3 = r, meaning that the radius of a sphere is equal to the volume divided by π, times 3/4, all taken to the 1/3 power (or the cube root.)If you have a sphere with a volume of 100 inches3, solve for the radius as follows: ((V/π)(3/4))1/3 = r ((100/π)(3/4))1/3 = r ((31.83)(3/4))1/3 = r (23.87)1/3 = r
2.88 in = r , Use the formula r = √(A/(4π)).
The surface area of a sphere is derived from the equation A = 4πr2.
Solving for the r variable yields √(A/(4π)) = r, meaning that the radius of a sphere is equal to the square root of the surface area divided by 4π.
You can also take (A/(4π)) to the 1/2 power for the same result.If you have a sphere with a surface area of 1,200 cm2, solve for the radius as follows: √(A/(4π)) = r √(1200/(4π)) = r √(300/(π)) = r √(95.49) = r
9.77 cm = r
About the Author
Timothy Webb
Creates helpful guides on home improvement to inspire and educate readers.
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