GMAT Quantitative Reasoning › DSQ: Calculating the volume of a tetrahedron
Note: Figure NOT drawn to scale.
The above figure shows a rectangular prism with an inscribed tetrahedron, or triangular pyramid, with vertices . What is the volume of the tetrahedron?
Statement 1:
Statement 2:
A tetrahedron is a solid with four triangular faces.
Give the volume of a tetrahedron.
Statement 1: The tetrahedron has four equilateral faces.
Statement 2: The surface area of the tetrahedron is .
In the above diagram, a tetrahedron - a triangular pyramid - with vertices is shown inside a cube. Give the volume of the tetrahedron.
Statement 1: The perimeter of Square is 16.
Statement 2: The area of is 8.
Note: Figure NOT drawn to scale.
Refer to the above figure, which shows a tetrahedron, or triangular pyramid. What is the volume of the tetrahedron?
Statement 1: is an isosceles triangle with area 64.
Statement 2: is an equilateral triangle with perimeter 48.
A regular tetrahedron is a solid with four faces, each of which is an equilateral triangle.
Give the volume of a regular tetrahedron.
Statement 1: Each edge has length 8.
Statement 2: Each face has area .
In the above diagram, a tetrahedron—a triangular pyramid—with vertices is shown inside a cube. Give the volume of the tetrahedron.
Statement 1: The cube can be inscribed inside a sphere with volume .
Statement 2: A sphere with surface area can be inscribed inside the cube.
Note: Figure NOT drawn to scale.
The above figure shows a rectangular prism with an inscribed tetrahedron, or triangular pyramid, with vertices . What is the volume of the tetrahedron?
Statement 1: Isosceles right triangle has area 32.
Statement 2:
A solid in three-dimensional coordinate space has four vertices, at points ,
,
, and
for some positive values of
. What is the volume of the solid?
Statement 1:
Statement 2:
A solid on the three-dimensional coordinate plane has four vertices, at points ,
,
, and
for some positive values of
. What is the volume of the solid?
Statement 1:
Statement 2:
A solid on the three-dimensional coordinate plane has four vertices, at points ,
,
, and
for some positive values of
. What is the volume of the solid?
Statement 1:
Statement 2: