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

- Former price

The price of an article is cut by 10℅, to restore it to the former value, by what percent the new price must be increased? - Diamond and diagonals

A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!) - Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap. - The diagram 2

The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm^{2}. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone - The sides 2

The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid. - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - 3rd dimension

The block has a surface of 42 dm^{2}and its dimensions are 3 dm and 2 dm. What is the third dimension? - Pile of sand

A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand. - Cincinnati

A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth. - Right Δ

Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle. - Cube in a sphere

The cube is inscribed in a sphere with volume 6116 cm^{3}. Determine the length of the edges of a cube. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - 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. - Square diagonal

Calculate length of the square diagonal if the perimeter is 476 cm. - 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. - R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm^{2}. What is its perimeter? - 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 ?. - Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm^{3}. What is the area of surface of the prism? - ISO triangle

Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.

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