# Square + body volume - math problems

1. Prism 4 sides The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
2. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
3. 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.
4. Right pyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
5. Bricks pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
6. Regular prism The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
7. Alien ship The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the larges
8. The aquarium The aquarium has a capacity of 18 liters. What is its height when the square bottom is 8 2/3 cm long?
9. 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.
10. 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. Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
12. Find the Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm.
13. Cube wall Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
14. The coil How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
15. Square pyramid Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
16. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
18. Cylinder horizontally The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
19. 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.
20. 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

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