Practice problems of the volume - page 48 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
- Thousand balls
We must create a thousand balls from a sphere with a diameter of 1 m. What will be their radius? - Volume of sphere
How many times does the volume of a sphere increase if its radius increases two times? - Cylindrical tank
9.6 hl of water is poured into a cylindrical tank with a bottom diameter of 1.2 m. What height in centimeters does the water reach? - 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? - Quadrilateral pyramid
We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base area 2/casing area 3/pyramid surface 4/volume of the pyramid - A family
A family of four consumes 220 liters of water a day. How many hectoliters of water are consumed by 68 tenants per day? - Quadrilateral pyramid,
A quadrilateral pyramid has a rectangular base with 24 cm and 13 cm dimensions. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid - Water level
What is the area of the pool's water level after filling 25 m³ of water level by 10 cm? a) 25 m² b) 250 m² c) 2500 dm² d) 25,000 cm2 - Milk cartons
How much paper do we need for 12 tetra packs with dimensions 6 cm, 11 cm, and 20 cm? Will 1 liter of milk fit in the box? - Hexagonal pyramid
Calculate a regular hexagonal pyramid's volume and surface area with a base edge a = 30 m and a side edge b = 50 m. - Quadrilateral pyramid
The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place. - Hexagonal 29141
Calculate the volume and surface of a regular hexagonal prism with a base edge a = 30 m and a side edge b = 50 m. - Reservoirs 29051
The three water reservoirs hold a total of 130 liters. Determine their volumes in m³. If the first fits 15 liters less than the second and 20 liters less than the third. - Solutions, mixtures
We have 2 liters of 20% solution available. How much 70% solution do we need to add to get a 30% solution? - Copper wire
What is the mass of 500 m of copper wire with a diameter of 1 mm, if ρ = 8.9 g/cm³? - Quadrilateral oblique prism
What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°? - Long drive
Calculate how much it costs to drive 150,000 km with an average consumption of 7 liters per 100 km and a fuel price of 1.2 € / l. - Quadrilateral pyramid
A regular quadrilateral pyramid has a volume of 24 dm³ and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid - The regular
The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms; the height of the prism is 24 cm. Calculate its volume. - Converting units
Health care professionals frequently convert from one system of measurement to another. Whether you are converting a metric measurement into the household system for a patient or converting within the metric system to enter data in a specific format, the
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