Virginia SOL Math / Grade 8 / Measurement & Geometry

8.MG.2

Surface Area & Volume of Pyramids & Cones

What you'll learn

  • Find the surface area of pyramids and cones
  • Find the volume of pyramids, cones, and spheres
  • Solve practical problems involving these solids

Words to know

Pyramid —
a solid with a polygon base and triangular faces meeting at a point
Cone —
a solid with a circular base tapering to a point
Sphere —
the set of all points a fixed distance from a center
Slant height —
the distance from the base edge to the apex along a face
Volume —
the amount of space a solid occupies

Why it matters These formulas let us find how much a scoop of ice cream, a grain silo, or a party hat holds or covers.

Worked examples

Model ItI do

Find the volume of a cone with radius 3 and height 10. Use 3.14 for pi.

The volume of a cone is one third times pi times radius squared times height. That is (1/3)(3.14)(3 squared)(10) = (1/3)(3.14)(9)(10) = (1/3)(282.6) = 94.2 cubic units.

Try It TogetherWe do

Find the volume of a sphere with radius 6. Use 3.14 for pi.

The volume of a sphere is four thirds times pi times radius cubed. That is (4/3)(3.14)(6 cubed) = (4/3)(3.14)(216) = (4/3)(678.24) = 904.32 cubic units.

Now YouYou do

Find the volume of a pyramid with a square base 4 by 4 and height 9.

Volume of a pyramid is one third times base area times height. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Find the volume of a pyramid with base area 12 and height 5.

  2. 2.Find the volume of a cone with radius 2 and height 9. Use 3.14 for pi.

  3. 3.A cone and cylinder share the same base and height. How many cones of water fill the cylinder?

On Level

The core Quick Check from the book.

  1. 1.Find the volume of a cone with radius 5 and height 12. Use 3.14 for pi.

  2. 2.Find the volume of a sphere with radius 3. Use 3.14 for pi.

  3. 3.Find the volume of a pyramid with base area 20 and height 6.

  4. 4.A cone and a cylinder share the same base and height. How many cones fill the cylinder?

  5. 5.Find the volume of a square pyramid with base edge 6 and height 10.

Challenge

Stretch your thinking.

  1. 1.Find the volume of a square pyramid with base edge 6 and height 8. Then double the height and state the new volume.

  2. 2.Find the volume of a sphere with radius 3. Use 3.14 for pi.

  3. 3.An ice-cream cone has radius 3 and height 12. A scoop is a sphere of radius 3 on top. Using 3.14 for pi, does the cone hold all the ice cream if it melts into it?