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

- Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Triangular prism

Calculate the surface of a regular triangular prism with a bottom edge 8 of a length of 5 meters and an appropriate height of 60 meters and prism height is 1 whole 4 meters. - Big cube

Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long. - The volume

The volume of a solid cylinder is 260 cm^{3}the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid - Alaska vs Montana

Alaska is the largest state in the United States and has a surface area of approximately 588,000 square miles. Montana has a surface area that is approximately 25% of the surface area of Alaska. What is the approximate surface area of Montana? - Axial section

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

The cuboid has a surface area 1771 cm^{2,}the length of its edges are in the ratio 5:2:4. Calculate the volume of the cuboid. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=10 and height v=18? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm^{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 254 cm^{2.} - 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 10×10×9 cm. Warren wants to cover with square paper with sides of 29 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. - 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? - 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?

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