A triangle has sides of length 2, 3 and 4. What is the radius of the circle that circumscribes the triangle?
A. 2.0
B. 2.5
C. 3.0
D. 3.5
The correct answer is: B
Rationale: The triangle is a right-angled triangle, therefore the hypotenuse is a diameter of the circumscribing circle.
A regular hexagon is inscribed inside a circle of radius 5. What is the length of one side of the hexagon?
A. 5
B. 10
C. 20
D. 25
The correct answer is: A
Rationale: Joining the centre of the hexagon to each of its vertices creates 6 equilateral triangles.
How many faces does a regular dodecahedron have?
A. 10
B. 12
C. 20
D. 24
The correct answer is: B
Rationale: The name "dodecahedron" is derived from Greek words meaning "twelve" and "seat" (i.e. face).
If two spheres have radii in the ratio 2:1, what is the ratio of their volumes?
A. 2:1
B. 4:1
C. 6:1
D. 8:1
The correct answer is: D
Rationale: The volume of a sphere is proportional to the cube of its radius.
A cube is inscribed inside a sphere. If the cube has a volume of 8, what is the volume of the sphere?
A. 4π
B. 6π
C. 8π
D. 12π
The correct answer is: B
Rationale: The diameter of the sphere is equal to the length of the diagonal of the cube, which is 2√3.
The angles of a triangle are in the ratio 2:3:4. What is the difference in degrees between the largest and smallest angle?
A. 20
B. 40
C. 60
D. 80
The correct answer is: C
Rationale: The angles of a triangle sum to 180 degrees.
What is the sum of the interior angles of a regular octagon?
A. 720
B. 900
C. 1080
D. 1440
The correct answer is: C
Rationale: An octagon can be split into 6 triangles, each with an angle sum of 180 degrees.
What is the maximum number of points of intersection between 4 distinct lines in a plane?
A. 4
B. 5
C. 6
D. 7
The correct answer is: C
Rationale: Each line can intersect with the 3 other lines.
A rectangular prism has a square base of side length 4 and a height of 6. What is the length of the longest line segment that can be contained wholly within the prism?
A. 6
B. 8
C. 10
D. 12
The correct answer is: C
Rationale: The longest line segment is a diagonal of the prism.
A line segment is drawn between two opposite corners of a cube with side length 4. What is the length of this line segment?
A. 4
B. 4√2
C. 4√3
D. 8
The correct answer is: C
Rationale: Applying the Pythagorean theorem twice gives the length of the line segment.