Problems for the calculation of the surface area of the solid object
- Water tank
A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
- Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
- Axial section
Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
The cuboid has a surface area 3380 cm2, the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid.
- Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
- 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.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
The cube has area of base 400 mm2. Calculate the edge length, volume and area of its surface.
Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
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.
- Cuboid diagonal
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.
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'
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″.
Gift box has rectangular shape with dimensions of 4×9×19 cm. Todd wants to cover with square paper with sides of 27 cm. How much paper left him?
- Cube zoom
How many percent we increase volume and surface of cube, if we magnify its edge by 61%.
Right triangle with legs 9 cm and 16 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
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?
Calculate the surface cube with edge 29 dm.
Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 50 cm high when head circumference is 47 cm.
- 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.