Practice problems of the volume - page 115 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: 2353
- Water
Mix 67 l of water with a temperature of 67 °C, 17 l warm of 32 °C, and 79 l water of 87 °C. What is the temperature of the mixed water immediately after mixing? - Cylinders
The area of the side of two cylinders is the same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume, and by how much? - Alcohol
How much 56% alcohol do we need to pour into 22 liters 78% alcohol to get p3% alcohol? How much 76% alcohol do we get? - Sea water
Mixing 62 kg of seawater with 84 kg rainwater is created water containing 3.1% salt. How much percent of seawater contains salt?
- Vinegar 2
How many percentages of vinegar solution will we get if we mix 3.5 liters of 5.8% and 5 liters of 7.6% vinegar? - Bath
In the bath is 30 liters of hot water. Then we added 36 liters of cold water at a temperature of 19 °C and decreased the temperature of water to 41 °C. What was the initial temperature of the hot water? - Solution
In 469 dl red solution is 84 dl red color, and in 102 dl blue solution is 52 dl blue color. How many dl of red and blue dl color solution must be mixed to get a mixture of 247 dl to contain 116 dl of color? - Spherical cap
From the sphere with a radius of 11 was a truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere? - Rectangular cuboid
The rectangular cuboid has a surface area 5447 cm², and its dimensions are in the ratio 2:4:1. Find the volume of this rectangular cuboid.
- 2x cone
Circular cone height 84 cm was cut plane parallel with the base. The volume of these two small cones is the same. Calculate the height of the smaller cone. - Cone
The 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. - Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Peroxide
How much-distilled water (in liters) must pharmacists pour into 300 ml of 23.6% solution of hydrogen peroxide to get 2.7% solution to gargle? - Vinegar
We must dilute 16 liters of 8.8% aqueous vinegar to 4.1% one. How much water is necessary to add?
- Cuboid
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges. - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Cone A2V
The cone's surface in the plane is a circular arc with a central angle of 126° and area 415 cm². Calculate the volume of a cone. - Axial section
The axial section of the cone is an equilateral triangle with an area 208 m². Calculate the volume of the cone. - Rotation
The right triangle with legs 11 cm and 18 cm rotates around the longer leg. Calculate the volume and surface area of the formed cone.
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Tip: Our volume units converter will help you convert volume units. See also more information on Wikipedia.