# Surface area + Pythagorean theorem - problems

- Axial section

Axial section of the cone is equilateral triangle with area 300 m^{2.}Calculate volume of the cone. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2.}Calculate the volume of a cone. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm^{2.} - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Cap

Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 50 cm high when head circumference is 47 cm. - Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r_{1}=37 cm, r_{2}=40 cm and its distance v=20 cm. - Pyramid roof

1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - 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 7 cm. - Regular quadrangular pyramid

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%. - 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. - 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. - Canopy

Mr Peter has metal roof cone shape with a height of 36 cm and radius 73 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 2.1 m^{2}? - Pyramid a+h

Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm. - Tetrahedral pyramid

Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm^{2}and deviation angle of the side edges from the plane of the base is 60 degrees. - 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. - Rotating cone II

Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm. - 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. - Pit

Pit has shape of a truncated pyramid with rectangular bases and is 2.8 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 0.3 l of green colour. How many liters of paint is needed when w - Hexagonal prism

The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!

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Pythagorean theorem is the base for the right triangle calculator.