# Examples for 9th grade - page 49

- The cone

The lateral surface area of the cone is 4 cm^{2,}the area of the base of the cone is 2 cm^{2.}Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci - Rhombus A2p

Rhombus area is 13 cm^{2}and its height is 5cm long . Determine a perimeter of this rhombus. - Triangle SSA

Construct a triangle ABC if |AB| = 5cm v_{a}= 3cm, CAB = 50 °. It is to create the analysis and construction steps. - Bath salts

Bath salt A weighs 900 grams and costs 36,40 CZK. Bath Salts B weighs 1000 grams, but costs 85 CZK. How much is a bath salt A cheaper than B one? - Miraculous tree

Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 8 days? - Tray

Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm. - Positive number z

Positive number z is 10% greater than the number y. How many % is y smaller than z? Report the result rounded to one decimal place. - Circular flowerbed

Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle. - Rectangular trapezoid

The rectangular trapezoid having bases length 3.2 cm and 62 mm. The shorter arm has a length 0.25 dm. Calculate the lengths of the diagonals and the second arm. - Swing

A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance? - Iron fence

One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m^{3.} - 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 7 cm. - The city

In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)? - The farmer

The farmer harvested 840 tons of grain in 2006, which was 44% less than in 2005, and one-fifth more than in 2004. How many tons of grain harvested in years 2005 and 2004? - Percentage of waste

In a square plate with side 42 cm we cut 4 same circles. Calculate the percentage of waste. - The chord

Calculate a chord length which the distance from the center of the circle (S, 20 cm) equals 7 cm. - Trapezoid - diagonal

Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm^{2.}What is the area of the trapezoid? - Cottages

The summer camp is 41 cottages. Rooms are for three and for four in them. How many of the 140 campers lives of three? - Tourist Jirka

Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey? - Parallelogram

The perimeter of the parallelogram is 202 cm. The length of one side is 1.2-times longer than the length of the shorter side. What is the length of sides of a parallelogram?

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