# Examples for 8th grade - page 60

- Tickets

On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)? - Pine wood

From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum - Cuboid

The volume of the cuboid is 245 cm^{3.}Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid? - Three numbers

Find three numbers so that the second number is 4 times greater than the first and the third is lower by 5 than the second number. Their sum is 67. - Aquarium volume

The aquarium has a cuboid shape and dimensions a = 0.3 m, b = 0.85 m, c =? , V = ?. What volume has a body, if after dipping into the aquarium water level rises by 28 mm? - Rectangle - desc circle

Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter. - Lawns

Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?. - String

Divide the string length 800 cm in ratio 1: 5 - Right triangle ABC

Calculate the perimeter and area of a right triangle ABC, if you know the length of legs 4 cm 5.5 cm and 6.8 cm is hypotenuse. - 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. - The hall

The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m^{2.}What were the original dimensions of the hall? - 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.}

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