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Right Triangular Prism |
Prisms and Pyramids
Volume is the amount of three-dimensional space an object occupies, in cubic units, within a container.
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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 |
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The volume of a pyramid is one-third
the area of its base times its height.
B = base of pyramid, h = height
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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. |
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 (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. |
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 (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. |
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 (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. |
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 (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. |
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