# Pythagorean theorem - examples - page 19

- Church roof 2

The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m^{2}of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste? - Chord circle

The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch. - Hypotenuse

Calculate the length of the hypotenuse of a right triangle with a cathetuses 71 cm and 49 cm long. - Body diagonal

Find the cube surface if its body diagonal has a size of 6 cm. - Stadium

A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter. - Axial cut

The cone surface is 388.84 cm^{2}, the axial cut is an equilateral triangle. Find the cone volume. - Cube in sphere

The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere. - The ladder

The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall? - Regular quadrilateral pyramid

Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. - Forces

Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant? - Kite

John a kite, which is diamond shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs paper on both sides and needs 5% of the paper for bending. - Circle's chords

In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle. - Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. - Diamond perimeter

Calculate the diamond circumference which area is 288 cm square and one diagonal has a size of 124 cm. - The ditch

Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch? - Circular ring

Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form. - Equilateral triangle

The equilateral triangle has a 23 cm long side. Calculate its content area. - Square

Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg? - Ladder

Ladder 10 meters long is staying against the wall so that its bottom edge is 6 meters away from the wall. What height reaches ladder? - Body diagonal

The cuboid has a volume of 32 cm^{3}. Its side surface area is double as one of the square bases. What is the length of the body diagonal?

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Pythagorean theorem is the base for the right triangle calculator.