Chapter 16: Surface Area and Volume 219
WORLDLY WISDOM
Volume is always measured in cubic units.
To find the volume of a rectangular prism with length of 15 inches, width of 9 inches, and height
of 14 inches, first find the area of the base, 15 v 9 = 135 square inches, and multiply the area of
the base by the height. 135 v 14 = 1890, so the volume of the rectangular prism is 1,890 cubic
inches.
The volume of a rectangular prism is still V = Bh, but because the area of B is length times width,
the volume of a rectangular prism is sometimes written as V = lwh.
CHECK POINT
Find the volume of each prism. V = Bh
- A cube 7 inches on each edge.
- A rectangular prism with edges of 12 cm, 21 cm, and 15 cm.
- A triangular prism 6 inches high, with a base that is a right triangle with legs
3 inches and 4 inches long and a hypotenuse 5 inches long.
- A pentagonal prism, 8 inches high, with a base that is a regular pentagon with
sides 15 inches long and an area of 387 square inches.
- A hexagonal prism 50 cm high with a base that is a regular hexagon with a
perimeter of 30 cm and an area of 65 square cm.
Pyramids
A pyramid is a polyhedron formed by one polygon, called the base, surrounded by triangles that
meet at a point. Like prisms, pyramids take their names from the polygon that forms the base.
If the base is a pentagon, it’s a pentagonal pyramid. If the base is a square, it’s a square pyramid,
and if the base is also a triangle, it’s a triangular pyramid.
DEFINITION
A pyramid is a polyhedron composed of a polygon for a base surrounded by triangles
that meet at a point.
