Practice problems of the volume - page 53 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: 2346
- Calculate 24881
Calculate a sphere's volume and surface area with a radius of 23dm. - Eight
Eight small Christmas balls with a radius of 1 cm have the same volume as one large Christmas ball. What has a bigger surface: eight small balls or one big ball? - Volumes 24771
The block and the cube have the same volumes = 216 cm³. The block has side lengths of b = 4 cm, c = 9 cm. Can they have the same side? - Trapezoidal 24731
Calculate how many candies fit in a box shaped like a 4-sided prism with a trapezoidal base with base dimensions of 20 cm and 3.2 cm. The distance between the bases is 50 mm. The container is 32 cm high, and 1 candy occupies 2.5 cm³ of volume.
- Cylinder in cube
Into a paper box in the shape of a cube with an edge of 10 cm is placed a can in the shape of a cylinder with a height of 10 cm and touching all the walls of the cube. What % of the volume of the cube can take up? - The water tank
The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank if we paint with 1 kg of paint 10 m²? - Quadrilateral 24541
There are 50 liters of water in a filled container in the shape of a regular quadrilateral prism. Determine the height of the water if the edge of the base a = 25 cm. - Calculate 24511
Calculate the height of the cylinder if d = 1.6 dm and V = 489 cm³. - Volleyball 24471
The radius of a volleyball is 10 cm. Calculate how many liters of air fit into an ideal inflated ball. Calculate how many square meters of leather material you need to make it.
- Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube. - AL wire
What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic? Please round to the nearest gram. - Trapezoidal prism
Calculate the volume of a prism with a trapezoidal base with side a = 6 dm, side c = 4 dm, and height of the prism = 8dm. The height of the trapezoid is va = 3dm. - Runcated pyramid teapot
The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot? - Millimeter 24231
Calculate the length of the wall diagonal of a cube with a volume of 7.40 square meters. Express the result to the nearest millimeter.
- Hectoliters of water
There are 942 hectoliters of water in a cylindrical tank with an inner diameter of 6 m. The water reaches two-thirds of the depth of the tank. Calculate its depth. - Cylindrical 24211
The cylindrical container contains 62.8 liters of water and is completely filled. The height of the container is half a meter. Calculate the bottom diameter. - Calculate 24201
Calculate the surface area, volume, and length of the body diagonal of a cube with an edge length of 4 dm. - Diameter 24181
What is the weight of a lead ball with a diameter of 3 cm if the density of lead is 11340 kg/m cubic? - Quadrilateral 24161
Calculate the volume of a quadrilateral prism whose base is an isosceles trapezoid with bases 10 cm and 4 cm, 6 cm apart. The height of the prism is 25 cm. How could the surface area be calculated?
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