Examples for 8th grade - page 74
- 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.
- Grass seeds
How many kg of grass seed is needed to be sowing a circular field with a diameter of 120 meters when the 1 m2 should be used 0.8 grams seeds?
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.
Calculate the content of the shaded part of square with side 43 cm.
- Concrete pipe
How much will cost cover a 6 m long concrete pipe with an outer radius 1.5 m and inner radius 0.8 meters if 1 m2 paint costs 24 €.
- 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
- Chord 2
Point A has distance 13 cm from the center of the circle with radius r = 5 cm. Calculate the length of the chord connecting the points T1 and T2 of contact of tangents led from point A to the circle.
- Volume and surface
Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
- Right triangle
Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
- Rectangular trapezoid
Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
- Two months
Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?
- 10 pieces
How to divide the circle into 10 parts (geometrically)?
- Metal alloy
What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel?
Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.
Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type?
- Triangle midpoints
Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.