7th grade (12y) + expression of a variable from formula - examples
- Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
- Midpoint 5
FM=3x-4, MG=5x-26, FG=? Point M is the midpoint of FG. Use the given information to find the missing measure or value.
- Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
The cube has area of base 256 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?
- Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 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
- Trapezoid ABCD v2
Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm2. What is the area of trapezoid ABCD?