# Examples for 9th grade

- 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 ? - Isosceles trapezoid

Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high. - Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. - Regular n-gon

In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon. - Inner angles

The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places. - Sequence 11

What is the nth term of this sequence 1,1/2,1/3,1/4,1/5 ? - Photocopier

A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page? - Arithmetic progression

In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ? - Water channel

The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo - Tricolors

From the colors - red, blue, green, black and white, create all possible tricolors. - Acres

Two hours 24 students harvested chestnuts on 36 acres. How many square meters harvested one student per hour? - Cuboid edges in ratio

Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm^{3}. - Trapezoidal prism

Calculate the surface of the quadrilateral prism ABCDA'B'C'D 'with the trapezoidal base ABCD. The height of the prism is 12 cm; ABCD trapezoidal data: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diagonal length is 7 cm. - Similarity coefficient

The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ". - Krkonose CZ

Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Cuboid height

What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic? - Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3}, a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Average speed 4

Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip? - Mirror

How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m.

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