# Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.

Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

1. Conical area A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
2. Trapezoidal prism Calculate the surface of the quadrilateral prism ABCDA'B'C'D 'with the trapezoidal base ABCD. The height of the prism is 12 cm; ABCD trapezoidal data: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diagonal length is 7 cm. L
3. Hexagon cut pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
4. Solid cuboid A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
5. Surface area of the top A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
6. Triangular prism Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
7. Sphere equation Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
9. Ratio of edges The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
10. 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.
11. Find the Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm.
12. Sand path How many m3 of sand is needed to fill the 1.5m wide path around a rectangular flowerbed of 8m and 14m if the sand layer is 6cm high?
13. The room The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
14. Square prism Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
15. Sphere from tree points Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
16. 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. Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
18. Find diagonal Find diagonal of cuboid with length=20m width=25m height=150m
19. Triangular prism Calculate the surface of a regular triangular prism with a bottom edge 8 of a length of 5 meters and an appropriate height of 60 meters and prism height is 1 whole 4 meters.
20. Body diagonal Calculate the volume and surface of the cube if the body diagonal measures 10 dm.

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