# Surface area - 8th grade (13y) - math problems

1. The cylinder 2 Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
2. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
3. Rectangular cuboid The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
4. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
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. Tereza The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
8. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
9. 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.
10. Prism Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 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
11. 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.
12. Cone Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
13. 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?
14. Cube zoom How many percents do we increase the volume and surface of the cube if we magnify its edge by 38 %?
15. Rotation The right triangle with legs 14 cm and 20 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone.
16. 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?
17. Pyramid roof 2/4 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?
18. 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.
19. Cylinder - basics Cylinder with base radius r = 45 dm and height h=22 dm. Calculate:
20. Tower How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?

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