 Volume (for Polyhedra) MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts  Right Triangular Prism Prisms and Pyramids Volume is the amount of three-dimensional space an object occupies, in cubic units, within a container. Right Rectangular Pyramid
 The volume of a prism is its base area times its height.   V = volume in cubic units;   B = area of the base in square units;    h = prism height in units Vprism = Bh

 The volume of a pyramid is one-third the area of its base times its height.   B = base of pyramid, h = height  Note: Actual dimensions have been rounded to nearest tenth, as needed. (Right Triangular Prism)
 1. Find the volume of this right triangular prism. Remember to show your work. Solution:   • Find the area of the triangular base. Since the base is a triangle, use A = ½ b• h.             A = ½ • 9 • 6 = 27 sq. units. • The prism's height = 12 units. • The prism volume formula is V = Bh, where B = base area and h = height of prism.             V = 27 sq. units • 12 units = 324 cubic units.   (Right Regular Triangular Pyramid)
 2. Find the volume of this right regular triangular pyramid. Remember to show your work. Solution:   • A "regular" triangular pyramid means that all three side of the triangular base are the same length (10 units), making the base an equilateral triangle. • Find the area of the triangular base. A = ½ b• h.             A = ½ • 10 • 8.7 = 43.5 sq. units. • The pyramid's height = 12 units. • The pyramid volume formula is V = (1/3)Bh.            V = (1/3)• 43.5 sq. units • 12 units = 174 cubic units.   (Right Trapezoidal Prism)
 3. Find the volume of this right trapezoidal prism. Remember to show your work. Solution:   • Find the area of the trapezoidal base by decomposing the trapezoid. A (triangle) + A(square) = ½ (3)(4) + (4)(4) = 22 sq. units. • The prism's height = 9 units. • The prism volume formula is V = Bh.   V = 22 sq. units • 9 units = 198 cubic units.   (Right Trapezoidal Pyramid)
 4. Find the volume of this right, trapezoidal pyramid. Remember to show your work. Solution:   • Find the area of the trapezoid base by decomposing. A(triangle) + A(rectangle) + A(triangle) = ½ (3)(4) + (4)(8) + ½(3)(4) = 44 sq. units • The pyramid's height = 12 units. • The pyramid's volume is V =(1/3)Bh.    V = (1/3) • 44 sq. units • 12 units = 176 cubic units.   (Composite Solid)
 5. Find the volume of this solid, composed of a right square prism and a right square pyramid. Remember to show your work. Solution:   • Find the volume of the right square prism. V = l • w • h = 8•8•8 = 512 cubic units • Find the volume of the right square pyramid. V = (1/3)•Bh = (1/3)•(8)(8)•9 = 192 cubic units • Find the volume of the composite solid. Add the two volumes.    V = 512 cu. units + 192 cu. units = 704 cubic units.  