# Examples for 9th grade - page 72

- Land - isosceles trapezoid

Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m. - Three numbers

What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8. - 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)? - Roof 8

How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof. - Church roof 2

The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m^{2}of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste? - Two numbers

We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers. - Chord circle

The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch. - Brick wall

Garden 70 m long and 48 m wide should surround with wall 2.1 meters high and 30 cm thick. Wall will be built on the garden ground. How many will we need bricks if to 1 m³ is required approximately 300 bricks? - Three-digit

How many three-digit natural numbers do not have the number 7? - Divisible by 5

How many three-digit odd numbers divisible by 5, which are in place ten's number 3? - Cuboid enlargement

By how many percent increases the volume of cuboid if its every dimension increases by 30%? - 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. - Angles in ratio

The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z. - Water reservoir

The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used. - AP 6

Calculate the first five items of an arithmetic sequence if it is given: a_{2}– a_{3}+ a_{5}= 20 a_{1}+ a_{6}= 38 - Tree shadow 3

A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ? - Body diagonal

Find the cube surface if its body diagonal has a size of 6 cm. - Balls

The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white? - Four friends

Four friends shared the money. Vasek got 1/4 of the total amount. Tonda received 1/3 of the rest of the money, Joe got a half from the second residue and Jirka left 80. How much money get together? - Axial cut

The cone surface is 388.84 cm^{2}, the axial cut is an equilateral triangle. Find the cone volume.

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