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/m3. 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.
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?
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
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 pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done?
How much you will pay CZK for laying tiles in a square room with a diagonal of 8 m if 1 m2 cost CZK 420?
- Height difference
What height difference overcome if we pass road 1 km long with a pitch21 per mille?
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.
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.
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 cm3 . 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 u1 = 22 cm and u2 = 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/m3