Practice problems of the volume - page 49 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
- Company car
Ms. Vaňková has a company car equipped with a multifunction indicator, on which she can monitor the average petrol consumption during individual rides. During the first ride, mostly in city traffic, it traveled 20.5 km, with an average consumption of 7.8L - Manufacturing 28591
A furniture manufacturing company consumes 124 cubic meters of spruce and oak lumber per month. Spruce lumber consumes three times more than oak lumber. How much spruce and oak lumber does the company use per month? - Triangular prism
The triangular prism has a base in the shape of a right triangle, the legs of which are 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²? - Weight
The kilogram weight has a volume of 116 ml. From which material is it probably made? Use substance density tables, e. G. mathematical-physical-chemical tables.
- Cylinder-shaped 28531
The diameter of the bottom of the cylinder-shaped tank is 6 m. Its volume is 1500 m³. What is the height of the tank to about two decimal places? - Parameters 28521
The basic parameters of the rotating cone are: Base radius 5 cm Cone height 12 cm and cone side 13 cm. Calculate: a/volume of the cone b/cone surface - Rotating 28501
Which bags shaped like the shell of a rotating cone can hold the most popcorn? The first bag has a height of 20 cm, and the length of its side is 24 cm. The second bag has a base radius of 10 cm and a height of 25 cm. - Quadrilateral 28491
Calculate the weight of a regular quadrilateral pyramid with a base edge of 4 cm in length and a body height of 6 cm if it is made of a material density of 8 g/cm³. - Ball-shaped 28481
How many square meters of material is needed to make a ball-shaped balloon with a volume of 950 m³?
- Aquarium 28461
The aquarium has a bottom in the shape of a square a = 8 dm. How many liters of water flowed into it if its level rose by 10 cm? - Gas sphere
The gas tank has the shape of a sphere with a diameter of 14 m. How many m³ of gas will fit in it? - Clay balls
How many can clay balls with a radius of 1 cm be made from a ball of clay with a radius of 8 cm? - Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
- Mixing 5
Carlos mixed 4/15 of chocolate syrup with 1/2 of milk. Determine the reasonable estimate of the total amount of liquid - Gas, lpg and diesel
Calculate how much it costs to drive 35000 km by car: a) a car with the consumption of 8l/100 km of LPG for 60 cents b) 7l/100 km of petrol for 1.33 euros c) 6 l/100 km of diesel for 1.2 euros. Calculate what is cheaper. - Four prisms
Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The prism base is a rhombus with a side length of 30 cm and a height of 27 cm. The height of t - Mixing paint with water
Mr. Adamek will paint. The purchased paint is diluted with water in a ratio of 1: 1.5. a) how many parts of water will add to 1 part of the paint b) how many liters of water the mission adds to 2 liters of paint - Flower boxes
How many m² of 10mm thick boards are needed to make 12 flower boxes? The dimensions of the box are 180,150, and 1500 mm.
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