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

- Cube in a sphere

The cube is inscribed in a sphere with volume 3234 cm^{3}. Determine the length of the edges of a cube. - Rectangular cuboid

The rectangular cuboid has a surface area 5334 cm^{2}, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid. - Square diagonal

Calculate length of the square diagonal if the perimeter is 476 cm. - 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. - 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. - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}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. - R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm^{2}. What is its perimeter? - Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm^{3}. What is the area of surface of the prism? - Right isosceles

Calculate area of the isosceles right triangle which perimeter is 41 cm. - Sphere A2V

Surface of the sphere is 241 mm^{2}. What is its volume? - 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? - Arc

Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m. - Square

If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm^{2}. Determine the side length of the original square. - Shape

Plane shape has a maximum area 677 mm^{2}. Calculate its perimeter if perimeter is the smallest possible. - Brass tube

The outer perimeter of brass tube (ρ = 8.5 g/cm^{3}) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness? - Cylinder

The cylinder surface is 922 dm^{2}, its height is equal to the radius of the base. Calculate height of this cylinder. - 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. - 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 - 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 8

The surface of the cube is 0.54 m^{2}. Calculate the length of the cube edge.

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