Square root + expression of a variable from formula - math problems

1. Cube in a sphere The cube is inscribed in a sphere with volume 3234 cm3. Determine the length of the edges of a cube.
2. 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.
3. Square diagonal Calculate length of the square diagonal if the perimeter is 476 cm.
4. 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.
5. Right triangle Legs of right are in ratio a:b = 2:8. Hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
6. Cone 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.
7. R Trapezium Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
8. 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?
9. Right isosceles Calculate area of the isosceles right triangle which perimeter is 41 cm.
10. Sphere A2V Surface of the sphere is 241 mm2. What is its volume?
11. Chord In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
12. Arc Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
13. Square If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
14. Shape Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
15. Brass tube The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
16. Cylinder The cylinder surface is 922 dm2, its height is equal to the radius of the base. Calculate height of this cylinder.
17. Tent Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
18. Trapezoid 15 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
19. 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,
20. Cube 8 The surface of the cube is 0.54 m2. Calculate the length of the cube edge.

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