What is the formula for a sphere?

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

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Take note that a sphere is a round three dimensional figure. All points on the surface of a sphere are the same distance from the center. The distance from the center of a sphere to its surface is called the radius.

Example of objects that have a shape of a sphere are marbles and basketballs.

To compute for the surface area of the sphere, use the formula:

`A = 4pir^2`

And to compute for its volume, apply the formula:

`V =4/3pir^3`

where r represents the radius.

chrisyhsun's profile pic

chrisyhsun | Student, College Freshman | (Level 1) Salutatorian

Posted on

I see that previous answers have provided equations for the surface area and volume of a sphere. I thought I would add to the answers above by writing about the equation for the points that compose a sphere in 3 dimensions. The equation for this is remarkably similar to the equation for a circle in 2 dimensions (for good reason, as slicing a sphere gives you a circle regardless of how it is cut). The equation for a sphere is (x – a)^2 + (y – b)^2 + (z – c)^2 = r^2 for a sphere with its center at point (a, b, c) and radius of length r on a standard x-y-z graph. (Compare this to the (x – a)^2 + (y – b)^2 = r^2 for a circle with center at (a, b) and radius of length r). Like a circle, this equation shows how the distance calculation of any point on the sphere to the center (the left side of the equation) is equal to the square of the length of the radius.

ik9744's profile pic

ik9744 | Student, Grade 9 | (Level 1) Valedictorian

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The formula for a sphere is:

Volume : 4/3*PI*r^3               [R to the 3rd power or cubed]

Surface : 4(pi)*r^2                 [R to the 2nd power or squared]

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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The volume for a sphere is: `4/3pir^3`

And for the surface area it is: `4pir^2`

 

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