# 8th grade (13y) + expression of a variable from formula - examples

- A report

Maricris can type a committee report in 5 hours. Jane helped Maricris and together they finished the report in 3 hours. How long would it take Jane to complete the report she had worked alone? - The garden

The garden has the shape of a rectangular trapezium. The bases have lengths of 27 meters and 36 meters, the trapezoid's height is 12 meters. Calculate how much fence will cost this garden if one meter costs 1.5 €? - Motorcyclist

From Trutnov, the motorcyclist started at an average speed of 60km/hour. At 12.30hrs the passenger car was started at a speed of 80km/hour. How many hours and at what distance from Trutnov will car catch a motorcycle? - Cube surface and volume

Find the surface of the cube with a volume of 27 dm^{3}. - Soldier

An experienced soldier digs a good trench in 30 hours. Two soldiers dug the same trench each 40 hours. How many hours will the ditch dig all three together? - Right Δ

Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle. - Cuboid

The cuboid has a surface area 7705 cm^{2}, the length of its edges are in the ratio 1:4:5. Calculate the volume of the cuboid. - 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. - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - Sea water

Mixing 34 kg of sea water with 34 kg rainwater is created water containing 3.4% salt. How many percent sea water contains salt? - 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. - Garden

Father dig up the garden in 9 hours. Son in 13 hours. How many hours take dig up the garden together? - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Cylinder - h

Cylinder volume is 215 cm^{3}. Base radius is 2 cm. Calculate the height of the cylinder. - Right triangle

Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm.

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