# Examples for 9th grade

- Nine-gon

Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm. - Liters od milk

The cylinder-shaped container contains 80 liters of milk. Milk level is 45 cm. How much milk will in the container, if level raise to height 72 cm? - Road - permille

5 km long road begins at an altitude 500 meters above sea level and ends at a altitude 521 ASL. How many permille road rises? - 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? - Paper box

Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m^{2}of the paper consumed 100 such boxes? - Water level

The glass container has a cuboid shape with dimensions of the bottom 24 cm and 12 cm. The height of water is 26 cm. Calculate the volume of the body, which are sunk into the water if the water level rise by 3 cm. - 3 days

Worker checked 2,950 products in 3 days. Second day checked 25% more than the first day. The third day 15% more products than the second day. How many products he checked in each day. - Earth's surface

The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land? - 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. - 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. - Parcel

parcel has a rectangular shape of a trapezoid with bases 12 m and 10 m and a height 8 m. On parcel was built object with a footprint an isosceles triangle shape with side 4 m and height three-quarters of a meter. What is the area of unbuild parcel? - The fence

I'm building a fence. Late is rounded up in semicircle. The tops of late in the field between the columns are to copy an imaginary circle. The tip of the first and last lath in the field is a circle whose radius is unknown. The length of the circle chord - Giant coin

From coinage metal was produced giant coin and was applied so much metal, such as production of 10 million actual coins. What has this giant coin diameter and thickness, if the ratio of diameter to thickness is the same as a real coin, which has a diamete - Trapezoid v3

The isosceles trapezoid has the angle at a firsst base 40 degrees less than the angle at second base. How large angles has this trapezoid ? - Trapezoid RT

The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumpti - 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? - Distance runner

Distance runner already climbed three fifths of the total route. Thus passed 90 km. How many km he have to stop? How long is his route? - Cuboid

Find the cuboid that has the same surface area as the volume. - Mom and daughter

Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter? - Right trapezoid

The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length 0.25 dm. Calculate the lengths of the diagonals and the second leg.

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