# 9th grade (14y) + expression of a variable from formula - examples

- Regular quadrangular pyramid

The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes? - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm. - Soaps

Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H - Rain

It rains at night. On 1 m^{2}of lake will drop 60 liters of water. How many cm will the lake level rise? - Equilateral triangle

Calculate the area of an equilateral triangle with circumference 72cm. - Surface of cubes

Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes? - The bulbs

The bulbs are connected serially two bulbs and one resistor. Each bulb has a resistivity of 100 ohms and resistor of 60 ohms The voltage source in the circuit is 24 volts. Do you know what voltage to measure on individual appliances? - Flying

The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable? - Diagonal to area

Calculate the area of a rectangle in which the length of the diagonal is 10 cm. - Perimeter of a rectangle

If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width? - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Trapezoid - intersection of diagonals

In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area. - Meat loses

Meat loses 18% of its weight by smoking. How much raw meat butcher used to manufacture 35 kilos of smoked? - The price

The price of the land increased by 17%. What was the original price of the land if it now costs 46800 €? - Right Δ

Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle. - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm. - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - Arc and segment

Calculate the length of circular arc l, area of the circular arc S_{1}and area of circular segment S_{2}. Radius of the circle is 33 and corresponding angle is ?.

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