# Unit conversion + Pythagorean theorem - math problems

#### Number of problems found: 43

• 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? The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
• The regular The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
• Truncated pyramid The concrete pedestal in the shape of a regular quadrilateral truncated pyramid has a height of 12 cm, the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base.
• 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?
• Cable car Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
• Cone - side Find the surface area and volume of the cone if its height is 125 mm and the side length is 17 cm.
• Sailboat The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
• Right angled triangle 3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
• Cone - from volume surface area The volume of the rotating cone is 1,018.87 dm3, its height is 120 cm. What is the surface area of the cone?
• Decagon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
• Circular segment Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
• Isosceles trapezoid The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?
• 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.
• 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?
• 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
• Square Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2? 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?
• Pine wood From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lu
• Support colum Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.

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