# Examples for 9th grade - page 64

- Aluminum wire

Aluminum wire of 3 mm diameter has a total weight of 1909 kg and a density of 2700 kg/m^{3.}How long is the wire bundle? - Rhombus IV

Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm. - 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? - Property

The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cost - Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - Triangular pyramid

Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm - Rectangular triangles

The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c - Locomotive

Locomotive pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done? - Tiles

How much you will pay CZK for laying tiles in a square room with a diagonal of 8 m if 1 m^{2}cost CZK 420? - Height difference

What height difference overcome if we pass road 1 km long with a pitch21 per mille? - Railway

Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent? - RT leg and perimeter

Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 188. - Jar

From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 6 cm and a jar diameter D is 8 cm. How to calculate how much water remains in the jar? - Internal and external angles

Calculate the remaining internal and external angles of a triangle, if you know the internal angle γ (gamma) = 34 degrees and one external angle is 78 degrees and 40 '. Determine what kind of triangle it is from the size of its angles. - Draw a trapezoid

Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task. - Triangle

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 177 b = 124 c = 63 - Equilateral cylinder

Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 221 cm^{3}. Calculate the surface area of the cylinder. - Rectangle and circle

The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long. - Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u_{1}= 22 cm and u_{2}= 15 cm. Prism height is twice base edge length. - Hollow sphere

Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m^{3}

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