# Pythagorean theorem + unit conversion - practice problems

#### Number of problems found: 47

- TV diagonal

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

Mr Peter has a metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs to paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m²? - 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 - Traffic cones

Forty identical traffic cones with a base diameter d = 3 dm and a height v = 6 dm should be painted on the outside with orange paint (without base). How many crowns do we pay for color? If we need 50 cm ^ 3 of paint to paint, 1m² and 1l of paint costs CZK - The roof

The roof of the house has the shape of a regular quadrilateral pyramid 5 m high and the edge of the base 7 m. How many tiles with a content of 540 cm² are needed? - Diagonals of a prism

The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base. - 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 - 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. - Prism

Right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 13 cm, has the same volume as a cube with an edge length of 3 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - 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. - Prism - box

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism. - The Scout Tent

The Scout Tent has a rectangular wooden underlay with dimensions of 220 cm and 150 cm. How much canvas is needed for a 170 cm high pyramid roof? - Support colum

Calculate the volume and surface of the support column that is shaped as a perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m. - Cone - from volume surface area

The volume of the rotating cone is 1,018.87 dm^{3}, and its height is 120 cm. What is the surface area of the cone? - 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? - Tetrahedral pyramid

Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm. - The quadrilateral pyramid

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. - 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. - 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.

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Pythagorean theorem is the base for the right triangle calculator. Pythagorean theorem - practice problems. Unit conversion - practice problems.