# Surface area + Pythagorean theorem - problems

1. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
2. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=10 and height v=18?
3. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone.
4. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
5. 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
6. Cone
Calculate volume and surface area of ​​the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
7. Cap
Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm.
8. Pyramid roof
1/3 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 9 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
9. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
10. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
12. Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
13. 4side pyramid
Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
14. Pyramid a+h
Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
15. Canopy
Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
16. Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
17. Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
18. Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
19. Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
20. Pit
Pit has shape of a truncated pyramid with rectangular bases and is 3.5 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.8 l of green colour. How many liters of paint is needed when w

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Pythagorean theorem is the base for the right triangle calculator.