How do you find the volume and surface area of a sphere?

Category: 3D Shapes »

Course: Geometry »

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Spheres

Although the sphere is a fierce adversary when it comes to sketching (thank goodness for Geogebra), calculating its volume and surface area are humble tasks.Spheres are three dimensional shapes, but they are defined as the collection of points in space that are equidistant from the center, and as such, only have one real measurement: the radius. Both volume and surface area of a sphere are defined only using its radius.

Formulas

The volume of a sphere is given by$$V = \frac{4\pi r^3}{3}$$The surface area of a sphere is given by$$S = 4 \pi r^2$$

Tips

• Volume is a three dimensional measure and needs to have cubic units
• Surface Area is a two dimensional measure and needs to have squared units
• For the Calc students in the room, the surface area of a sphere is the derivative of the volume
• The volume formula is more commonly needed than surface area, and typically needs to be memorized
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