Height From the Surface
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 39 of 62.
If the surface area and the radius are known, the height is fixed. The height appears only in the curved side's term, so the equation is linear in h.
This cylinder has radius 3 and surface area 48π. The rule says 48×pi = 2×pi×3^2 + 2×pi×3×h. Divide everything by π: 48 = 18 + 6×h. Then 30 = 6×h and h = 5.
As with volumes, the board writes the equation already divided by π. Work out the ends' term first, then subtract it.
Challenge
The cylinder's surface area is 80π and its radius is 4. Write the equation from the figure and solve it for h.
Then press Check.
Try it yourself
Use the figure to find h
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: Pyramids2Volume of Prisms
Volume of a CuboidVolume of a PrismAny Triangle EndA Missing EdgeRecap: Prism Volume8Surface Area of Cylinders
Unrolling a CylinderHeight From the SurfaceRadius From the SurfaceEnough for the Volume?Recap: Cylinder Surfaces3Cylinders
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