Examples for the calculation of the surface area of ​​the solid object

1. Base of prism The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
2. Seat How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds?
3. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
4. 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.
5. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
6. 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.
7. 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.
8. Tereza The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
9. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
10. 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.
11. 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
12. 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.
13. 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°.
14. 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?
15. Cube zoom How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
16. 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.
17. 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 the sheet is required to cover the top of the tower if we count 8% of the sheet waste?
18. Cube Calculate the surface cube with edge 11 dm.
19. 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?
20. 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?

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.