Pythagorean theorem + expression of a variable from formula - problems - page 4

1. Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
2. Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
4. Pentagon
Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
5. Two cyclists
Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start?
6. Rectangle
The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
7. Right triangle eq2
Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
8. Billboard
Rectangular billboard is 2.5 m long with a diagonal 2.8 m long. Calculate the perimeter and the content area of the billboard.
9. Diagonal of the rectangle
Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
10. Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
11. Two diagonals
The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
12. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
13. Church roof 2
The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
14. Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
15. Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
16. Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
17. Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
18. Circle's chords
In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.