7th grade (12y) + expression of a variable from formula - examples
- A company
A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
- A cylindrical tank
A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank?
- Rectangle 45
The perimeter of a rectangle is 60cm. If the length of the rectangle is 20cm. a)find the width b)find the area.
- Sugar production
From 1 ton of beet, 150 kg of sugar is produced. To clean 1 ton of sugar 450 kg of lime is consumed. Calculate how many kgs of lime is consumed when processing 1 ton of sugar beet?
- Area to volume
If the surface area of a cube is 486, find its volume.
- Marriage sttus
In our city, there are 3/5 of the women married to 2/3 of the men. Find what part of the population is free.
The sum of all cube edges is 30cm. Find the surface area of the cube.
- 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 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.