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

- Masquerade ball

Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm^{2}. - Prism 4 sides

The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters - Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap. - Prism 4 sides

Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - 3rd dimension

The block has a surface of 42 dm^{2}and its dimensions are 3 dm and 2 dm. What is the third dimension? - Axial section

Axial section of the cone is equilateral triangle with area 208 dm^{2}. Calculate volume of the cone. - Rectangular cuboid

The rectangular cuboid has a surface area 5334 cm^{2}, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6? - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm^{2}. - 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. - Tereza

The cube has area of base 256 mm^{2}. Calculate the edge length, volume and area of its surface. - Sphere

Surface of the sphere is 2820 cm^{2}, weight is 71 kg. What is its density? - Gutter

How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees. - Prism

Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 10 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 = 15 cm and side of cone with the base has angle 52°. - Present

Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him? - Cube zoom

How many percent we increase volume and surface of cube, if we magnify its edge by 38%. - Rotation

Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.

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