Surface of a Sphere
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 48 of 62.
A sphere cannot be unrolled flat, so its surface area came from another of Archimedes' discoveries. The sphere's surface has exactly the area of the curved side of the cylinder it fits in.
That cylinder has radius r and height 2r, so its curved side is 2×pi×r × 2×r = 4×pi×r^2. For this sphere of radius 3: 4 × pi × 3^2 = 36×pi. That is four times the area of a circle through the sphere's centre.
The rule is Surface area of a sphere: SA = 4×pi×r^2. The radius is squared now, because a surface is an area, not a volume.
Challenge
Find the exact surface area of the sphere, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis 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: Pyramids7Surface Area of Prisms
Nets and Surface AreaVolume or Surface Area?A Missing Edge AgainTriangular PrismsThe Hidden Side FirstRecap: Prism Surfaces10Spheres Outside
Surface of a SphereSurface of a HemisphereRadius From the SurfaceSurface to VolumeRecap: Spheres Outside2Volume 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