Body volume + expression of a variable from formula - examples
- A company
A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
- Quadrangular pyramid
The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
- Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
- A cylindrical tank
A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank?
- The volume 2
The volume of a cube is 27 cubic meters. Find the height of the cube.
- Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
- Area to volume
If the surface area of a cube is 486, find its volume.
- Cube in a sphere
The cube is inscribed in a sphere with volume 8818 cm3. Determine the length of the edges of a cube.
- 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.
- 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.
The cube has area of base 225 mm2. Calculate the edge length, volume and area of its surface.
Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
- Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
- 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?
- Cylinder - h
Cylinder volume is 215 cm3. Base radius is 2 cm. Calculate the height of the cylinder.
- Sphere A2V
Surface of the sphere is 241 mm2. What is its volume?
- Hollow sphere
Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
- Spherical segment
Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.
- Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.