# Examples for 9th grade

- Sphere radius

The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm. - Right triangle trigonometrics

Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - Map scale

On a 1:1000 scale map is a rectangular land of 4.2 cm and 5.8 cm. What is the area of this land in square meters? - Sales of products

For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold? - Sides od triangle

Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm. - Socks

One pair of socks worth CZK 27. Set of 3 pairs of these socks are sold with 10% discount. How many we will pay CZK for two offered sets of socks? - Unknown number 23

Find 2/3 of unknown number, which is two thirds of the 99. - Storm

So far, a storm has traveled 35 miles in 1/2 hour in direction straight to observer. If it is currently 5:00 p. M. And the storm is 105 miles away from you, at what time will the storm reach you? Explain how you solved the problem. - Salt

Sea water containing 5% salt. How many kg of fresh water necessary to pour into 40 kg of sea water so that the salinity fell to 2%? - Trucks

Three lorries droved bricks. One drove n bricks at once, second m less bricks than the first and third 300 bricks more the first lorry. The first lorry went 4 times a day the largest went 3 times a day and the smallest 5 times a day. How many bricks b - Trapezoid

How long are the trapezoid bases with area 24 cm^{2}and height 3 cm. One base is 3 times longer than the shorter. - Savings

Paul has a by half greater savings than half Stanley, but the same savings as Radek. Staney save 120 CZK less than Radek. What savings have 3 boys together? - Rope

How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)? - Bags

The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights. - Family

Mom is 42 years old and her daughters 13 and 19. After how many years will mother as old as her daughter together? - Basic form

Expressed the ratios of values in the basic form: 0,5 t : 1,2 kg 200 l : 0,15 m^{3}12 t : 3600 kg 500 kg : 2,5 t 0,9 kg : 500 g 3,6 m : 240 cm 1200 mm : 2,4 m 300 l : 0,3 m^{3}6 min 30 s : 900 s - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Tree shadow

The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)? - Percentages 5

$5.25 is 7 1/2% of what number? - Trapezoid MO-5-Z8

Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm^{2}. What is the area of the trapezoid KLMN?

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