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Questions and Answers
A square pyramid has a base side length of 6 cm and a height of 8 cm. What is its volume?
A square pyramid has a base side length of 6 cm and a height of 8 cm. What is its volume?
- 144 cm
- 96 cm (correct)
- 72 cm
- 288 cm
A cone has a circular base with a radius of 5 inches and a height of 12 inches. What is the volume of the cone?
A cone has a circular base with a radius of 5 inches and a height of 12 inches. What is the volume of the cone?
- 300 in
- 60 in
- 100 in (correct)
- 25 in
An oblique pyramid has a base area of 45 cm and a perpendicular height of 9 cm. Find its volume.
An oblique pyramid has a base area of 45 cm and a perpendicular height of 9 cm. Find its volume.
- 15 cm
- 405 cm
- 135 cm (correct)
- 225 cm
A triangular pyramid has a base that is a right triangle with legs of length 3 cm and 4 cm. If the height of the pyramid is 5 cm, what is its volume?
A triangular pyramid has a base that is a right triangle with legs of length 3 cm and 4 cm. If the height of the pyramid is 5 cm, what is its volume?
A cone has a volume of $24$ cubic inches and a height of 2 inches. What is the radius of the cone's base?
A cone has a volume of $24$ cubic inches and a height of 2 inches. What is the radius of the cone's base?
A composite solid consists of a cylinder with a cone on top. The cylinder has a radius of 3 cm and a height of 5 cm. The cone has the same radius and a height of 4 cm. What is the total volume of the solid?
A composite solid consists of a cylinder with a cone on top. The cylinder has a radius of 3 cm and a height of 5 cm. The cone has the same radius and a height of 4 cm. What is the total volume of the solid?
If a pyramid and a cone have the same base area and the same height, how do their volumes compare?
If a pyramid and a cone have the same base area and the same height, how do their volumes compare?
A regular hexagonal pyramid has a base area of 60 cm and a height of 10 cm. What is its volume?
A regular hexagonal pyramid has a base area of 60 cm and a height of 10 cm. What is its volume?
A cone has a slant height of 13 cm and a radius of 5 cm. What is its volume?
A cone has a slant height of 13 cm and a radius of 5 cm. What is its volume?
The volume of a cone is $48$ cubic units. If the radius and height are equal, find the radius.
The volume of a cone is $48$ cubic units. If the radius and height are equal, find the radius.
What is the volume of a pyramid with a square base of side length 4 and a height of 6?
What is the volume of a pyramid with a square base of side length 4 and a height of 6?
A cone has a height of 9 units and a base radius of 2 units. Find its volume.
A cone has a height of 9 units and a base radius of 2 units. Find its volume.
An ice cream cone is filled exactly level to the top of the cone. The diameter of the cone is 6 cm and the height is 10 cm. If the ice cream melts completely, what volume will the melted ice cream occupy?
An ice cream cone is filled exactly level to the top of the cone. The diameter of the cone is 6 cm and the height is 10 cm. If the ice cream melts completely, what volume will the melted ice cream occupy?
A square pyramid has a base with side length 5 cm and a height of 6 cm. Determine its volume.
A square pyramid has a base with side length 5 cm and a height of 6 cm. Determine its volume.
A triangular pyramid has a height of 9 inches. The triangular base has a base of 4 inches and a corresponding height of 5 inches. What is the volume of the triangular pyramid?
A triangular pyramid has a height of 9 inches. The triangular base has a base of 4 inches and a corresponding height of 5 inches. What is the volume of the triangular pyramid?
A right circular cone has a height of 12 cm. The diameter of the base is 10 cm. What is the volume of the cone?
A right circular cone has a height of 12 cm. The diameter of the base is 10 cm. What is the volume of the cone?
A square pyramid has a volume of 432 $cm^3$. Its height is 9 cm. What is the length of one side of its square base?
A square pyramid has a volume of 432 $cm^3$. Its height is 9 cm. What is the length of one side of its square base?
A party hat is in the shape of a cone. The base has a diameter of 12 cm. The height is 14 cm. How much material is needed to construct the party hat?
A party hat is in the shape of a cone. The base has a diameter of 12 cm. The height is 14 cm. How much material is needed to construct the party hat?
The volume of a right cone is 384 $ft.^3$ and the radius measures 8 ft. Find the height of the cone.
The volume of a right cone is 384 $ft.^3$ and the radius measures 8 ft. Find the height of the cone.
The base of a pyramid is a rectangle with sides 6 cm and 8 cm. If the volume of the pyramid is 112 $cm^3$, find its height.
The base of a pyramid is a rectangle with sides 6 cm and 8 cm. If the volume of the pyramid is 112 $cm^3$, find its height.
Flashcards
Volume of a Pyramid
Volume of a Pyramid
The volume of a pyramid is calculated by one third times the base area times the height (V = 1/3Bh).
Volume of a Cone
Volume of a Cone
The volume of a cone equals one third times the base area times the height (V = 1/3 * πr²h).
Cavalieri's Principle
Cavalieri's Principle
Cavalieri's Principle states that if two solids have the same height and the same cross-sectional area at every level, then they have the same volume.
Volume of a Cylinder
Volume of a Cylinder
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Solid of Revolution
Solid of Revolution
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Arc Length
Arc Length
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Study Notes
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The volume of a pyramid equals one third the product of the area of the base and the height of the pyramid
V = (1/3)Bh
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According to Cavalieri's Principle, the volume formula applies to all pyramids, even oblique ones
-
The height of an oblique pyramid refers to the length of the perpendicular line from the vertex to the base plane
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The volume of a cone is one third the product of the area of the base and the height of the cone
- V = (1/3)Bh, or V = (1/3)πr²h
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This formula is applicable to all cones, including oblique cones
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