Surface area - 9th grade (14y) - examples

  1. Conical area
    cones_2 A right angled triangle has sides a=11 and b=10 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
  2. Quadrangular pyramid
    komoly Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
  3. Three cubes
    cubes3 The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
  4. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
  5. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
  6. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  7. 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 137 cm2.
  8. Sphere
    1sphere Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
  9. Gutter
    okap 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.
  10. Cuboid diagonal
    cube_2 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.
  11. Prism
    3b_hranol 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'
  12. Cone
    cone-blue 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″.
  13. Cube zoom
    krychle_1 How many percent we increase volume and surface of cube, if we magnify its edge by 61%.
  14. Rotation
    cone_1 Right triangle with legs 9 cm and 16 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
  15. Tower
    HexagonalPyramid_4 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 m2 of sheet is required to cover the top of the tower if we count 12% of the sheet waste?
  16. Sphere slices
    sphere_slices Calculate volume and surface of a sphere, if the radii of parallel cuts r1=37 cm, r2=40 cm and its distance v=20 cm.
  17. Prism X
    hranol The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 48000 cm3. What is the area of surface of the prism?
  18. Pyramid roof
    pyramid_roof 1/3 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
  19. Cylinder - basics
    cylinder Cylinder with base radius r = 37 cm and height h=74 cm. Calculate:
  20. Rotary cone
    cone_3 The volume of the rotation of the cone is 104 cm3 and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone.

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