IMO Geometry 2

Question 1

A cube has a side length of 4 cm. What is its volume?

Accepted Answer

64 cm³

Answer

Volume of a cube = side³ = 4³ = 64 cm³.

Question 2

Two angles of a triangle are 55° and 75°. What is the third angle?

Accepted Answer

50°

Answer

Third angle = 180° − 55° − 75° = 50°, since all angles in a triangle sum to 180°.

Question 3

What is the name of a polygon with 6 sides?

Accepted Answer

Hexagon

Answer

A hexagon is a polygon with exactly six sides and six angles.

Question 4

A right-angled triangle has legs of length 3 cm and 4 cm. What is the length of the hypotenuse?

Accepted Answer

5 cm

Answer

By the Pythagorean theorem: hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Question 5

What is the circumference of a circle with diameter 14 cm? (Use π ≈ 22/7)

Accepted Answer

44 cm

Answer

Circumference = π × d = (22/7) × 14 = 44 cm.

IMO - International Mathematics Olympiad Practice Test