Body volume + expression of a variable from the formula - math problems
Number of problems found: 199
- Water tank
300hl of water was filled into the tank 12 m long and 6 m wide. How high does it reach?
- The volume
The volume of the sphere is 1 m ^ 3, what is its surface?
- Equilateral cone
We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down?
- Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
- Volume of sphere
How many times does the volume of a sphere increase if its radius increases 2 ×?
- Cone from cube
The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m3
- From plasticine
Michael modeled from plasticine a 15 cm high pyramid with a rectangular base with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter d = 10 cm. How tall was Janka's cone?
Calculate the surface and volume of the cone that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee.
- Hemisphere cut
Calculate the volume of the spherical layer that remains from the hemisphere after the 3 cm section is cut. The height of the hemisphere is 10 cm.
- Length of the edge
Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
- Pentagonal pyramid
Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm.
- The cylinder
The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder.
- Height of the cylinder
The cylinder volume is 150 dm cubic, the base diameter is 100 cm. What is the height of the cylinder?
- 9-gon pyramid
Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
- Triangular prism - regular
The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
- Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
- Angle of cone
The cone has a base diameter of 1.5 m. The angle at the main apex of the axial section is 86°. Calculate the volume of the cone.
- Aquarium height
How high does the water in the aquarium reach, if there are 36 liters of water in it? The length of the aquarium is 60 cm and the width is 4 dm.
- Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
- Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.