Volume - high school - math problems

Magnified cube
If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube.
Embankment
The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m³ of soil is in the embankment?
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.
Permille of alcohol
I have 2 per mille of alcohol in my blood. How many milliliters is it when I have 5 liters of blood?
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.
Kostka
Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
Cuboid and ratio
Find the dimensions of a cuboid having a volume of 810 cm³ if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
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.
Tetrahedral pyramid 8
Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p
Lemonade
Iva added one liter of 100% fruit juice to 3 liters of water. She left two liters of it for Alice and Beata. She added two more liters of water to the remain two liters of lemonade and offered it to other friends. a. What percentage of juice did Alena an
Quadrilateral prism
Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
Triangular prism,
The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm³ (l).
The ball
The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
Cone side
Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
Pool
How many hl of water is in a cuboid pool (a = 25m, b = 8m) if the area of the wetted walls is 279.2 m²?
Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.