SAT II Math II : SAT Subject Test in Math II
Study concepts, example questions & explanations for SAT II Math II
All SAT II Math II Resources
Example Questions
Example Question #1 : Surface Area
Find the surface area of a cube if the area of one of the square faces is 
Write the formula for the surface area of a cube.
The area of a square side is already given. Substitute that as the 
The answer is:
Example Question #21 : 3 Dimensional Geometry
A regular tetrahedron has four congruent faces, each of which is an equilateral triangle.
The total surface area of a given regular tetrahedron is 600 square centimeters. To the nearest tenth of a centimeter, what is the length of each edge?
The total surface area of the tetrahedron is 600 square centimeters; since the tetrahedron comprises four congruent faces, each has area 
The area of an equilateral triangle is given by the formula
Set 
Example Question #2 : Faces, Face Area, And Vertices
A regular octahedron has eight congruent faces, each of which is an equilateral triangle.
The total surface area of a given regular octahedron is 400 square centimeters. To the nearest tenth of a centimeter, what is the length of each edge?
The total surface area of the octahedron is 400 square centimeters; since the octahedron comprises eight congruent faces, each has area 
The area of an equilateral triangle is given by the formula
Set 
Example Question #1 : Faces, Face Area, And Vertices
A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle.
A given regular icosahedron has edges of length four inches. Give the total surface area of the icosahedron.
The area of an equilateral triangle is given by the formula
Since there are twenty equilateral triangles that comprise the surface of the icosahedron, the total surface area is
Substitute 
Example Question #31 : 3 Dimensional Geometry
How many faces does a polyhedron with nine vertices and sixteen edges have?
By Euler's Formula, the relationship between the number of vertices 
Set 
The polyhedron has nine faces.
Example Question #3 : Faces, Face Area, And Vertices
How many edges does a polyhedron with eight vertices and twelve faces have?
Insufficient information is given to answer the question.
By Euler's Formula, the relationship between the number of vertices 
Set 
The polyhedron has eighteen edges.
Example Question #5 : Faces, Face Area, And Vertices
How many faces does a polyhedron with ten vertices and fifteen edges have?
Insufficient information is given to answer the question.
By Euler's Formula, the relationship between the number of vertices
Set 
The polyhedron has seven faces.
Example Question #6 : Faces, Face Area, And Vertices
How many faces does a polyhedron with ten vertices and sixteen edges have?
By Euler's Formula, the relationship between the number of vertices
Set 
The polyhedron has eight faces.
Example Question #1 : Faces, Face Area, And Vertices
A convex polyhedron with eighteen faces and forty edges has how many vertices?
The number of vertices, edges, and faces of a convex polygon—
Therefore, set 
The polyhedron has twenty-four faces.
Example Question #5 : Faces, Face Area, And Vertices
How many edges does a polyhedron with fourteen vertices and five faces have?
By Euler's Formula, the relationship between the number of vertices
Set 
The polyhedron has seventeen edges.
All SAT II Math II Resources
