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This printable supports Common Core Mathematics Standard GMD.A.3

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# 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. $65","333","333 \ "ft"^3$
2. $91","636","272 \ "ft"^3$
3. $19","636","272 \ "ft"^3$
4. $695","272 \ "ft"^3$
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. $1","340","000 \ "ft"^3$
2. $420","000 \ "ft"^3$
3. $1","450","000 \ "ft"^3$
4. $1","420","000 \ "ft"^3$
3.
A rectangular pyramid shaped roof has a volume of $4,000 \ "ft"^3$ 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 $50 \ "ft"^3$ of granite and is 6 feet high. What is the area of the base of the sculpture?
1. $5 \ "ft"$
2. $25 \ "ft"$
3. $5 \ "ft"^2$
4. $25 \ "ft"^2$
5.
A rectangular pyramid is 253 ft by 372 ft and 132 ft tall. What is the volume of the pyramid?
1. $4,104,141 \ "ft"^3$
2. $3,265,124 \ "ft"^3$
3. $4,008,333 \ "ft"^3$
4. $4,141,104 \ "ft"^3$
6.
A pool with a fountain is the shape of an inverted pyramid. The pool must be $25 \ m$ square and can hold $2,500 \ m^3$. How deep must it be in the middle?
1. $12 \ m$
2. $16 \ m$
3. $11 \ m$
4. $26 \ m$
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. $64 \ "ft"^3$
2. $213 \ "ft"^3$
3. $71 \ "ft"^3$
4. $17 \ "ft"^3$
8.
A pyramid shaped roof covers a house which is 36 ft X 36 ft. If the attic contains $4320 \ "ft"^3$ of air, how high is the peak?
1. $10 \ "ft"$
2. $8 \ "ft"$
3. $12 \ "ft"$
4. $11.5 \ "ft"$
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. $10","103","452 \ "ft"^3$
2. $10","131","452 \ "ft"^3$
3. $10","743","760 \ "ft"^3$
4. $1","743","760 \ "ft"^3$
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. $59.2 \ "ft"^3$
2. $153.6 \ "ft"^3$
3. $49.8 \ "ft"^3$
4. $51.2 \ "ft"^3$
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