Practice problems of the volume - page 114 of 118
Volume is the measure of the space that a body fills or occupies. The basic SI unit of volume is the cubic meter. It is the volume of a cube with an edge of one meter, i.e., 1 m x 1 m x 1 m. Significant another unit is 1 l (one liter), 1 m3 = 1000 l applies. One hectoliter (1 hl) is 100 liters.Volume is always the third power of length. Or volume = area times length. For example, the volume of the cube is a3, and the prism's volume is S*h (the area of the base times the height). The volume of rotating bodies (sphere, cone) can be derived in high school by integration. The pyramid's volume is always 1/3 of the prism's volume. We calculate the volume of the truncated bodies either with a formula or simply by subtracting the volumes of the two bodies.
Number of problems found: 2355
- Cone
Calculate the volume and surface area of the cone with a diameter of the base d=15 cm and the side of the cone with the base has angle 52°. - Lid
What is the weight of the concrete cover (lid) to round shape well with a diameter 1.8 m if the thickness of the cover is 11 cm? 1 m³ of concrete weighs 2190 kg. - Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1° - Pharmacy
At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 4 L of the 48-percent solution. What amount of solution from each container is needed to mix?
- Fertilizer
Mr. Gherkin uses for fertilization 10% solution of fertilizer. 5 liters of it still left. How much water must be added to the solution to make only the 7% solution? - Trough
How many liters of water per second can go via trough, which has a cross-section of a semicircle with a radius of 0.5 m and water speed is 142 cm per second? - Building
Lenka has 22 cubes for constructing a building comprising three cubes in height, the width of two cubes, and the length of four cubes. Is she able to build a building with these cubes? - Road embankment
Road embankment has a cross-section shape of an isosceles trapezoid with bases 5 m and 7 m and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters? - Tetrahedron
Calculate the height and volume of a regular tetrahedron whose edge has a length of 13 cm.
- Tereza
The cube has an area of base 144 mm². Calculate the edge length, volume, and area of its surface. - Pool
Mr. Peter builds a pool shape of a four-sided prism with a rhombus base in the garden. The base edge length is 8 m, and the distance between the opposite walls of the pool is 7 m. The estimated depth is 144 cm. How many hectoliters of water consume Mr. Pe - Cu wire
Copper wire has a length l = 820 m and diameter d = 10 mm. Calculate the weight if the density of copper is ρ = 8500 kg/m³. Please result round to one decimal place. - Beer
Which beer is better to drink: small beer (0.3 L) for 0.67 € or large (0.5 L) for 1.81 €? - Prism
A right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 6 cm, has the same volume as a cube with an edge length of 1 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
- Spherical segment
The spherical segment with height h=2 has a volume of V=112. Calculate the radius of the sphere of which is cut this segment. - Rotary cone
A rotary cone whose height is equal to the circumference of the base has a volume 229 cm³. Calculate the radius of the base circle and the height of the cone. - Cylinder - h
The cylinder volume is 140 cm³. The base radius is 7 cm. Calculate the height of the cylinder. - Sea water
Seawater contains about 5% salt. How many dm³ of distilled water must we pour into 39 dm³ of seawater to get water with 1.6% salt? - Pillar
Calculate the volume of the pillar shape of a regular tetrahedral truncated pyramid if his square has sides a = 19, b = 27, and height is h = 48.
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