Surface to Volume

Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 51 of 62.

The radius is the bridge between everything a sphere measures. Given the surface area, find the radius, then the volume.

$A sphere with surface area 36 pi$

This sphere has surface area 36π. Step one: 36×pi = 4×pi×r^2 gives r = 3. Step two: 4/3 × pi × 3^3 = 36×pi. The volume is 36π as well, because radius 3 is the one radius where the two numbers match.

On the board, tap the radius and pick the surface rule, then tap the sphere and pick Volume of a sphere.

Challenge

The sphere's surface area is 100π. Find its volume, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

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 Vertices Prisms and Cylinders Pyramids and Cones Height or Slant Height?Spheres and Hemispheres Recap: Parts of Solids

4Pyramids

Volume of a Pyramid The Slant Height Height From the Slant Height From the Volume Recap: Pyramids

7Surface Area of Prisms

Nets and Surface Area Volume or Surface Area?A Missing Edge Again Triangular Prisms The Hidden Side First Recap: Prism Surfaces

10Spheres Outside

Surface of a Sphere Surface of a Hemisphere Radius From the SurfaceSurface to VolumeRecap: Spheres Outside

3Cylinders

Volume of a Cylinder Height From the Volume Radius From the Volume Enough to Find It?Recap: Cylinders

6Spheres and Hemispheres

Volume of a Sphere Half a Sphere Radius From the Volume Sphere in a Cylinder Recap: Spheres

9Pyramids and Cones Outside

Surface of a Pyramid Slant Height First Surface of a Cone The Cone: Slant First Recap: Pyramid Surfaces

12Final Challenges

Final: The Clay Cone Final: The Water Tank Final: The Model Pyramid Final: The Tent Final: The Paint Can