# Surface area - 8th grade (13y) - examples

- Iron ball

The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm^{3}. - Half-sphere roof

The roof above the castle tower has the shape of a 12.8 m diameter half-sphere. What is the cost of this roof, if the cost of 1 square meter is 12 euros and 40 cents? - Regular triangular pyramid

Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters - Quadrangular pyramid

The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area. - 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 254 cm^{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 = 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 - 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. - Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm^{3}. What is the area of surface of the prism? - 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?

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