April 2021

A closed conical tank has a base diameter of 2 m and is 5 m tall. When standing in upright position, the water in the tank is 3 m deep. How deep will the water stand in the tank when in inverted position?

Three circles of different diameter are tangent externally. The triangle formed by the line joining their centers has sides 16 cm, 20 cm, and 24 cm, respectively. Find the area of the smallest circle in square cm.

In a bowling game, how many ways can the 10 pins fall in the first throw?

A sphere of radius 18 inches is cut by two parallel planes that are 16 inches apart. Find the volume on the sphere included between these cutting planes if the radius of one of the circles cut is 15 inches.

The total surface area of a regular tetrahedron is 339.482 cm². Find the measure of the edge of this tetrahedron.

The sides of a triangle measure 10 cm, 14 cm, and 8 cm, respectively. What is the smallest interior angle of this triangle?

A certain lotto game consists of 30 different balls numbered 1 to 30. If five balls are drawn at random without replacement, how many possible winning combinations can be made?

A hemispherical dome is 16 meters in diameter. If the bottom 1-meter strip of the dome’s surface painted, what is the total painted area?

A polygon has 104 diagonals. How many sides have this polygon?

A circle having a radius of 18 cm is cut by a chord 5 cm from the center. What is the area of the of the smaller segment?