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

  1. Equilateral cylinder
    sphere_in_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.
  2. Triangular prism
    prism_4 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.
  3. Big cube
    cubes_23 Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long.
  4. The volume
    cuboid_17 The volume of a solid cylinder is 260 cm3 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
  5. Alaska vs Montana
    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?
  6. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  7. Cuboid
    cuboid_1 The cuboid has a surface area 1771 cm2, the length of its edges are in the ratio 5:2:4. Calculate the volume of the cuboid.
  8. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=10 and height v=18?
  9. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone.
  10. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
  11. Sphere
    1sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
  12. Gutter
    okap 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.
  13. Cuboid diagonal
    cube_2 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.
  14. Prism
    3b_hranol 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
  15. Cone
    cone-blue 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°.
  16. Present
    prezent 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?
  17. Cube zoom
    krychle_1 How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
  18. Rotation
    cone_1 Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
  19. Pyramid roof
    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?
  20. Prism X
    Cuboid_simple The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?

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