Volume - high school - math problems

Number of problems found: 217

Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the volume of the segment. What is the distance of the cutting plane from the center of the sphere?
The water barrel
The water barrel weighs 122 kg. If we pour 75% of the water out of it, it will weigh 35 kg. What is the weight of the barrel?
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?
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.
Water mixing
We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C?
In the dairy
There were three times more packages of milk in the dairy than half a liter. When sold 10 liter and ten half-liter containers, four times more liters remained than half-liter packages. How many packages were there originally?
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?
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.
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 and
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).
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.
The ball
The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?