# Unit conversion + Pythagorean theorem - math problems

#### Number of problems found: 45

- Dig water well

Mr. Zeman digging a well. Its diameter is 120 cm and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out? - Cable car

Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m. - Decagon

Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m - Is right triangle

Find out if the triangle ABC (with right angle at the vertex C) is right if: a) a = 3dm, b = 40cm, c = 0.5m b) a = 8dm, b = 1.2m, c = 6dm - The conical

The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it? - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length. - Cross road

From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes? - TV diagonal

Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9? - The hemisphere

The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees? - Right trapezoid

The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length 0.25 dm. Calculate the lengths of the diagonals and the second leg. - Pyramid a+h

Calculate the pyramid's volume and surface area with the edge and height a = 26 cm. h = 3 dm. - Journey

Charles and Eva stands in front of his house, Charles went to school south at speed 5.4 km/h, Eva went to the store on a bicycle eastwards at speed 21.6 km/h. How far apart they are after 10 minutes? - Rotating cone

Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm. - What percentage

What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km - Glass mosaic

How many dm^{2}glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%. - Prism

Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m. - Cone - side

Find the cone's surface area and volume if its height is 125 mm and the side length is 17 cm. - Two cyclists

Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start? - Track arc

Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)? - Tent

Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.

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