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

1. Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
3. Axial section
Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
4. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
5. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
6. Cone A2V
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. Sphere
The surface of the sphere is 2820 cm2, and weight is 71 kg. What is its density?
8. 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.
9. 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
10. 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.
11. 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°.
12. Cube zoom
How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
13. Rotation
Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
14. Tower
The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of sheet is required to cover the top of the tower if we count 8% of the sheet waste?
15. Prism X
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?
16. 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?
17. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
18. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
19. Cylinder - basics
Cylinder with base radius r = 45 dm and height h=22 dm. Calculate:
20. Rotary cone
The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.

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