Units - math word problems

Central angle
What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?
Runcated pyramid teapot
The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?
Cyclist 12
What is the average speed of a cycle traveling at 20 km in 60 minutes in km/h?
Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
Interior angles
In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles.
Adam
Adam has half the money in his right pocket than in his left pocket. If he transferred 40 crowns from the left pocket to the right, he would have the same in both pockets. Calculate how many crowns does Adam have in his left pocket more than in his right?
Observation tower
From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower?
Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
Length of the arc
What is the length of the arc of a circle k (S, r=68mm), which belongs to a central angle of 78°?
Triangular prism
Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
Five tractors
Five tractors plow the fields in 4.8 hours. How long will it take to plow the field when, after an hour and a half of work, two tractor drivers have been called up for another task?
Triangle from median
Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
Two sides paint
The door has the shape of a rectangle with dimensions of 260cm and 170cm. How many cans of paint will be needed to paint this door if one can of paint cover 2m2 of the area? We paint the doors on both sides.
Two hemispheres
In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)?
Wire fence
The wire fence around the garden is 160 m long. One side of the garden is three times longer than the other. How many meters do the individual sides of the garden measure?
The half life
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives?
Average height
There are twice as many girls in the class as there are boys. The average height of girls is 177 cm, boys 186 cm. What is the average height of students in this class?
Tourist route
How long is the tourist route when tourists crossed four-sevenths of the way on foot, crossed the bus twice less than on foot and passed the last 14 kilometers by boat.
My father
My father cut 78 slats on the fence. The shortest of them was 97 cm long, the longer one was 102 cm long. What was the total length of the slats in cm?
Interior angles
Calculate the interior angles of a triangle that are in the ratio 2: 3: 4.

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