# 9th grade (14y) + expression of a variable from formula - examples

1. Ratio of sides Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
2. Lateral surface area The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
3. Rectangular trapezoid In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.
4. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
5. Right Δ A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
6. Cube in a sphere The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
7. Cone A2V Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
8. 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.
9. Square diagonal Calculate length of the square diagonal if the perimeter is 476 cm.
10. 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.
11. 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.
12. R Trapezium Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
13. 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 33 and corresponding angle is ?.
14. Prism X The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
15. 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.
16. Rhombus 2 Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
17. Right isosceles Calculate area of the isosceles right triangle which perimeter is 41 cm.
18. Square diagonal Calculate the length of diagonal of the square with side a = 23 cm.
19. Cylinder - h Cylinder volume is 215 cm3. Base radius is 2 cm. Calculate the height of the cylinder.
20. Truncated cone Calculate the height of the rotating truncated cone with volume V = 1115 cm3 and a base radii r1 = 7.9 cm and r2 = 9.7 cm.

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