Prism + square - examples

1. Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
2. Logs
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
3. Prism
Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 15 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
4. Present
Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
5. Prism
Three cubes are glued into prism, sum of the lengths of all its edges is 115 cm. What is the length of one edge of the original cube?
6. Surface and volume od cuboid
Content area of the square base of cuboid is Sp = 36 cm2 and its height 80 mm. Determine its surface area and volume.
7. Rectangle pool
Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
8. Prism
Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
9. Quadrangular prism
The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
10. Quadrangular prism
Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
11. 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.
12. Wood lumber
Wooden lumber is 4 m long and has a cross section square with side 15 cm. Calculate: a) the volume of lumber b) the weight of the lumber if 1 m3 weighs 790 kg
13. Angle of diagonal
Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
14. Find the
Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm.
15. Base of house
Calculate the volume of the bases of a square house, if the base depth is 1.2 m, the width is 40 cm and their outer circumference is 40.7 m.
16. Regular prism
The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
17. Density of the concrete
Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.
18. The aquarium
The aquarium has a capacity of 18 liters. What is its height when the square bottom is 8 2/3 cm long?
19. Square prism
A square prism has a base with a length of 23 centimeters, what is the area in square centimeters of the base of the prism?

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