7th grade (12y) + expression of a variable from formula - examples
Three-quarters of boats are white, 1/7 are blue and 9 are red. How many boats do we have?
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 dm3.
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?
The cuboid has a surface area 7705 cm2, the length of its edges are in the ratio 1:4:5. Calculate the volume of the cuboid.
The cube has area of base 225 mm2. Calculate the edge length, volume and area of its surface.
- 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.
The theater has in each row with 19 seats. Ticket to the first 10 rows is for 30 USD. In next rows is for 15 USD. The theater was completely sold out. Revenue was 12255 USD. How many rows are in the theater?
Circular cone of height 15 cm and volume 5699 cm3 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?
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.
How big is area of circle if its circumference is 80.6 cm?
Equilateral triangle with side 40 cm has the same perimeter as an isosceles triangle with arm of 45 cm. Calculate the base x of an isosceles triangle.
Trapezoid garden has parallel sides 19 m and 24 m. Its area is 193.5 square meters. What is the width of the garden?
- Cylinder - h
Cylinder volume is 215 cm3. Base radius is 2 cm. Calculate the height of the cylinder.
- Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
- BMI index
Calculate BMI (body mass index, an index indicating obesity, overweight, normal weight, underweight) man weighing m = 71 kg and height h = 170 cm. Index is calculated according to equation (formula): ? With BMI index is possible to compare people of diff