Radius From the Volume
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 14 of 62.
When a sphere's volume is known, the formula gives the radius. The last step undoes a cube, so you take a cube root: the number that, multiplied by itself three times, gives what you have.
This sphere holds 288π. The formula says 288×pi = 4/3 × pi × r^3. Cancel the π and multiply by 3/4: r^3 = 216. Since 6 × 6 × 6 = 216, the radius is 6.
A cube root, unlike a square root, has only one real answer, so there is no negative radius to throw away. On the board, the moves take the cube root for you once r³ stands alone.
Challenge
The ball holds 972π. Write the equation from the figure and solve it for its radius r.
Then press Check.
Try it yourself
Use the figure to find r
This lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Surface Area & Volume
1Solids and Their Parts
Faces, Edges and VerticesPrisms and CylindersPyramids and ConesHeight or Slant Height?Spheres and HemispheresRecap: Parts of Solids4Pyramids
Volume of a PyramidThe Slant HeightHeight From the SlantHeight From the VolumeRecap: Pyramids2Volume of Prisms
Volume of a CuboidVolume of a PrismAny Triangle EndA Missing EdgeRecap: Prism Volume3Cylinders
Volume of a CylinderHeight From the VolumeRadius From the VolumeEnough to Find It?Recap: Cylinders6Spheres and Hemispheres
Volume of a SphereHalf a SphereRadius From the VolumeSphere in a CylinderRecap: Spheres9Pyramids and Cones Outside
Surface of a PyramidSlant Height FirstSurface of a ConeThe Cone: Slant FirstRecap: Pyramid Surfaces