Practice problems of the volume - page 54 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 24011
There is a cylinder with a base radius of 3 cm and a height of 12 cm. Calculate a) cylinder surface b) cylinder volume - Triangular 24001
The tent's floor consists of a square with a side of 2.4 m, and the front and back wall is an isosceles triangle with a height of 1.6 m. Calculate the volume of air in the tent in liters. (Laid triangular prism.) - Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - Quadrilateral 23911
Calculate the volume of a regular quadrilateral pyramid, which has the size of the base edge a = 12 cm and a height of 11 cm.
- Quadrilateral 23891
A cylinder with the maximum possible base was ground from a wooden regular quadrilateral prism (edge 2.8 cm, height 7.5 cm). What percentage of the material was wasted as waste? What percentage would it be if the height of the prism were twice as large? - Quadrilateral 23881
Calculate the height of a regular quadrilateral prism whose base is a rhombus. The edge in the base is 7 cm long, the opposite edges are 5 cm apart, and we also know that the entire body has a volume of 1dm³. - Dimensions 23841
The cube-shaped potato peel waste bin is 80 cm high. How many liters of waste can we put into it if we know that the dimensions of the base are 40 cm and 50 cm, the basket is already full to exactly half its height, and as soon as the waste reaches the li - Measures 23791
The volume of the block is 144 cm³. The base measures 3 cm and 4 cm. How big is the body diagonal? - Centimeter 23781
Calculate the diameter of a cylinder 7.5 dm high with a volume of 0.6 hl. Express the result to the nearest centimeter.
- Identical cubes
From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm? - Calculate 23411
The prism with a diamond base has one base diagonal of 20 cm and a base edge of 26 cm. The edge of the base is 2:3 to the height of the prism. Calculate the volume of the prism. - Measuring 23281
We have a box with dimensions of 20cm, 16cm, and 8cm. How many cubes can fit in it if the cube has a size of 4cm? - Cube-shaped 23041
A pint of sugar weighs 800 g. How many tons of sugar will fit in a 100cm cube-shaped box? - Calculate 23031
The pool has sides of 5m 2m, and the water was 100hl. Calculate the height of the water in the pool.
- Originally 22951
The tank originally had 7 m³ of gasoline. We gradually pumped out 3hl, 3000dm3, and 700 liters of gasoline. How many liters of petrol is left in the tank? - Volume and surface area
Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm. - Cylinder-shaped 22643
The cylinder-shaped container contains 80 l of water and is filled. The height of the container is 70 cm. Calculate the diameter of the bottom of the container. - Planet Earth
What is the weight of the planet Earth if its average density is ρ = 2.5 g/cm³? - What is bigger?
Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
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