# Examples for 9th grade - page 57

- 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. - 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? - Two boxes-cubes

Two boxes cube with edges a=74 cm and b = 91 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge? - Silver medal

To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part? - Annulus

Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus. - Sphere area

A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere. - 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? - 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. - Surface area

The volume of a cone is 1000 cm^{3}and the content area of the axis cut is 100 cm^{2.}Calculate the surface area of the cone. - Chord 3

What is the radius of the circle where the chord is 2/3 of the radius from the center and has a length of 10 cm? - 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? - 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? - 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 would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 54, 71 and 44 meters. Find a suitable way to determine the. - Cardboard box

We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal - Repair company

The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 6 residue cars. How many total cars company repaired? - 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.

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