Volume of Pyramids (Grades 11-12)

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Volume of Pyramids

1. 
The great pyramid of Giza has a height of 481 feet and a square base with a width of 756 feet. If it is solid inside, what volume of rock is in it?
  1. [math]65,333,333 \ ft^3[/math]
  2. [math]91,636,272 \ ft^3[/math]
  3. [math]19,636,272 \ ft^3[/math]
  4. [math]695,272 \ ft^3[/math]
2. 
A pyramid has a base of 200 ft by 250 ft and a height of 87 ft. Inside the pyramid is a room in the shape a of a pyramid which measures 50 ft by 60 ft and 30 ft high. What volume of stone is used in the structure?
  1. [math]1,340,000 \ "ft"^3[/math]
  2. [math]420,000 \ "ft"^3[/math]
  3. [math]1,450,000 \ "ft"^3[/math]
  4. [math]1,420,000 \ "ft"^3[/math]
3. 
A rectangular pyramid shaped roof has a volume of [math]4,000 \ "ft"^3[/math] and a width to length ratio of 3:4. If the roof height is 10 ft, what is the length?
  1. 40 ft
  2. 30 ft
  3. 35 ft
  4. 65 ft
4. 
A square pyramid sculpture contains [math]50 \ ft^3[/math] of granite and is 6 feet high. What is the area of the base of the sculpture?
  1. [math]5 \ ft[/math]
  2. [math]25 \ ft[/math]
  3. [math]5 \ ft^2[/math]
  4. [math]25 \ ft^2[/math]
5. 
A rectangular pyramid is 253 ft by 372 ft and 132 ft tall. What is the volume of the pyramid?
  1. [math]4,104,141 \ "ft"^3[/math]
  2. [math]3,265,124 \ "ft"^3[/math]
  3. [math]4,008,333 \ "ft"^3[/math]
  4. [math]4,141,104 \ "ft"^3[/math]
6. 
A pool with a fountain is the shape of an inverted pyramid. The pool must be [math]25 \ m[/math] square and can hold [math]2,500 \ m^3[/math]. How deep must it be in the middle?
  1. [math]12 \ m[/math]
  2. [math]16 \ m[/math]
  3. [math]11 \ m[/math]
  4. [math]26 \ m[/math]
7. 
Sound damping foam used in recording studios is often composed of many square pyramids aligned edge to edge. Each pyramid is 4 in X 4 in X 4 in. What volume of foam would be required to cover the walls and ceiling of a studio which is 16 ft X 12 ft X 8 ft? (The ceiling is 8 ft high.)
  1. [math]64 \ "ft"^3[/math]
  2. [math]213 \ "ft"^3[/math]
  3. [math]71 \ "ft"^3[/math]
  4. [math]17 \ "ft"^3[/math]
8. 
A pyramid shaped roof covers a house which is 36 ft X 36 ft. If the attic contains [math]4320 \ "ft"^3[/math] of air, how high is the peak?
  1. [math]10 \ "ft"[/math]
  2. [math]8 \ "ft"[/math]
  3. [math]12 \ "ft"[/math]
  4. [math]11.5 \ "ft"[/math]
9. 
An ancient pyramid is 232 feet long, 183 feet wide and 130 feet tall. The interior cavity is a rectangular prism 80 feet long, 60 feet wide and 20 feet high. What volume of stone is in the pyramid?
  1. [math]10,103,452 \ ft^3[/math]
  2. [math]10,131,452 \ ft^3[/math]
  3. [math]10,743,760 \ ft^3[/math]
  4. [math]1,743,760 \ ft^3[/math]
10. 
A hedge is trimmed in the shape of a pyramid. The hedge is 8 feet square at the base and 6 feet high. If the shrub takes up 40% of the volume of the hedge, what volume of shrubbery is in the hedge?
  1. [math]59.2 \ ft^3[/math]
  2. [math]153.6 \ ft^3[/math]
  3. [math]49.8 \ ft^3[/math]
  4. [math]51.2 \ ft^3[/math]

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