Letters in the Lengths
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 56 of 62.
A length can be given as an expression, like x + 2. The formula still works: put the expression in where the length goes, and solve for x.
This cylinder has radius 3, height x + 2 and volume 63π. The rule gives 63 = 3^2 × (x + 2) once π is divided out, so 7 = x + 2 and x = 5. The height is 7.
Read the question to the end: sometimes it asks for x, sometimes for the length itself. Here x is 5 and the height is 7.
Challenge
The prism's ends are right triangles with legs 6 and 4. Its length is x + 4 and its volume is 120. Write the equation from the figure and solve it for x.
Then press Check.
Try it yourself
Use the figure to find x
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 Surfaces11Mixed Solids
Solids From SolidsA Spinning TopWhich Lengths?Letters in the LengthsRecap: Mixed Solids3Cylinders
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