# Examples for 9th grade

- The perimeter

The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX? - Two heights and a side

Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm and height to side b: vb = 4 cm. - Performance

Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together? - Bulbs and electricity

In the sports hall, 875 identical light bulbs light for 2 hours. How long does it take for 100 such light bulbs to consume the same amount of electricity? - 40% volume

40% volume with 104 uph (units per labor hour) 8 people working. What is the volume? - Angle of diagonal

Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - An oil

An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters. - Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Scientific notation

Approximately 7.5x10^{5}gallons of water flow over a waterfall each second. There are 8.6x10^{4}seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day. - Resistance

A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor. - Triangles

Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle? - Lampshade

The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm^{2}of material will we need when we 10% is waste? - Ditch

Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth. - 15 teachers

15 teachers teach for a combined amount of 128 days over a period of 64 days. What is this expressed as a percentage? - Blocks

There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there? - Area of iso-trap

Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other. - Bricklayers

When a bricklayer works himself to redeem the house in 8 days, the other bricklayer will be finished in 10 days. How long will it take to make 3 such houses together? - A square

A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal. - Ratio of edges

The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Big cube

Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long.

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