# Problems for the calculation of the surface area of the solid object

- Water tank

A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water. - Cylindrical container

An open-topped cylindrical container has a volume of V = 3140 cm^{3.}Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Axial section

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

The cuboid has a surface area 3380 cm^{2,}the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid. - 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.} - Tereza

The cube has area of base 400 mm^{2.}Calculate the edge length, volume and area of its surface. - Sphere

Surface of the sphere is 2260 cm^{2,}weight is 52.2 kg. What is its density? - Gutter

How much metal is needed for production 37 pieces of gutter pipes with the diameter 16 cm and length of 1 m? The plate bends add 7% of the material. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees. - 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' - Cone

Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″. - Present

Gift box has rectangular shape with dimensions of 4×9×19 cm. Todd wants to cover with square paper with sides of 27 cm. How much paper left him? - Cube zoom

How many percent we increase volume and surface of cube, if we magnify its edge by 61%. - Rotation

Right triangle with legs 9 cm and 16 cm rotate around longer leg. Calculate the volume and surface area of the formed cone. - Tower

The top of the tower is a regular hexagonal pyramid with base edge 9.2 meters long and a height 9.6 meters. How many m^{2}of sheet is required to cover the top of the tower if we count 12% of the sheet waste? - Cube

Calculate the surface cube with edge 29 dm. - 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.

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