# Cone + Pythagorean theorem - examples

1. Axial section Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
2. Cone A2V Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
3. 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°.
4. 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.
5. 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?
6. Cut and cone Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
7. Rotating cone II Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
8. Cone and the ratio Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
9. Sphere and cone Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
10. Angle of deviation The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
11. Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
12. Lamp cone Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
13. Area of the cone Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.
14. Rotating cone Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
15. Hexagon rotation A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
16. Truncated cone 5 The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
17. 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?
18. Axial cut The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
19. Truncated cone 3 The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang.
20. Cone Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.

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Pythagorean theorem is the base for the right triangle calculator.