Practice problems of the volume - page 37 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: 2355
- Consider
Consider all square prisms with a height of 10 cm. If x is the measurement of the base edge in cm, and y is the prism's volume in cm³. Graph the function - Calculate 43951
Calculate the radius of the base of the cylinder with a volume of 10 dm³ and a height of 15 cm. - Truncated 43851
The pit has the shape of a regular truncated 4-sided pyramid, the base edges of which are 14m, 10m, and the depth is 6m. Calculate how many m³ of soil were removed when we dug this pit. - Gallons and quarts
5 gallons 2 quarts − 1 gallon 3 quarts = (Hint: 4 quarts equals 1 gallon. )
- Transported 43451
A sandpit on a playground is shaped like a circle with a diameter of 3 meters and a depth of 25cm. How many cubic meters of sand are needed? Determine the weight of the transported sand if 1 m³ of sand weighs 800 kg. - The square
The square oak board (with density ρ = 700 kg/m3) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board? - Specified 43301
The water tank has the shape of a block. The bottom of the tank is square, with a side length of 3 m. There are 22,500 liters of water in the tank. To what height in meters does the water in the tank reach the specified amount? - Cone-shaped 43291
Calculate the volume and weight of a pile of cone-shaped sand with a diameter of 8m and a height of v = 4.5m, the density of sand is 1500kg / M cubic - The aluminum
We placed the aluminum object with a weight of 0.80 kg and a temperature of 250°C in the water with a weight of 1.6 kg and a temperature of 23°C. What is the system temperature after reaching equilibrium? We assume that the heat exchange occurred only bet
- The bath
The bath has water with a volume of 220 l and a temperature of 65°C. Find the mass m2 of water at 15°C to be poured, so the resulting temperature in the bath will be 40°C. We neglect the heat exchange between water and the environment. The mass - Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - The inflated
The inflated gymnastic ball should have a diameter of 65 cm. How many times do we have to pump air into a full-blown ball with a bicycle inflator to inflate it if the working volume of the inflator is a cylinder with an inner diameter of 2 cm and a height - The granite ball
What is the weight of a granite ball with a radius of 60 cm if 1 m³ of granite weighs 2.7 tons?
- Three friends
John, Peter, and Pablo each carried a 24 liters bucket full of water down the hill. After they reached the bottom, John's bucket was only 3/4 full, Peter's bucket was 2/3 full, and Pablo's was 1/6 full. How many liters of water did they spill altogether o - Honey 2
The baker has 3/4 liter of honey and decided to bake a few honeycombs and biscuits from it. He needed 1/6 liter of honey for honeycombs and 1/4 liter for biscuits. How much honey did she have left after baking honeycombs and biscuits? - A glass
A glass holds 3/4 cups. A jug holds 12 cups. How many glasses can be filled? - A 14.5-gallon
A 14.5-gallon gasoline tank is 3/4 full. How many gallons will it take to fill the tank? Write your answer as a mixed number. - Solution 42531
What strong solution is created by mixing 3 liters of 30% solution and 2 liters of 70% solution?
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