9th grade (14y) + expression of a variable from formula - examples
The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
- Body diagonal
Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
- Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
- Finding the base
Find unknown base of percent: 12.5 percent of what = 16 ?
- IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 26 cm, c = |CD| = 5 cm and legs b = d = |BC| = |AD| = 19 cm.
- 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.
- Arc and segment
Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 49 and corresponding angle is ?.
- Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 48000 cm3. 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 128 mm.
- Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel.
- 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 129 cm3. Base radius is 3 cm. Calculate the height of the cylinder.
- Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
- Cone and the ratio
Rotational cone has a height 28 cm and the ratio of the base surface to lateral surface is 4: 7. Calculate a surface of the base and the lateral surface.
- 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.
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
- Hollow sphere
Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
- Cathethus and the inscribed circle
In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
- Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
In a circle with radius r=11 cm is chord 4× longer than its distance from the center. What is the length of the chord?