Enough for the Volume?
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 41 of 62.
A question can give a measure you did not expect. A cylinder's surface area and its height say nothing directly about its volume, but they fix the radius, and the radius with the height fixes the volume.
This cylinder is 4 high with surface area 42π. The surface area rule fixes the radius, 3, as in the last lesson. Then the volume rule has the radius and the height. So yes, there is enough: two steps get the volume.
To decide, ask which formulas link what you know to what you want, one step at a time. If a chain of rules reaches it, the answer is Yes.
Challenge
The cylinder is 7 high and its surface area is 36π. Is there enough to find its volume? Answer, and if Yes, find it. Then press Check.
Try it yourself
Is there enough information?
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