Practice problems of the volume - page 47 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: 2354
- Exponential decay
A tank contains 55 liters of water. Water is flowing out at the rate of 7% per minute. How long does it take to drain the tank? - Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - Unknown metal
The prism made of unknown metal has dimensions of 3 cm by 3 cm by 5 cm and a weight of 121 g. What metal is it? Write its chemical symbol. - Brick wall
What is the weight of a solid brick wall that is 30 cm wide, 4 m long, and 2 m high? The density of the brick is 1500 kg per cubic meter.
- Surface and volume
Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long. - Deciliters 30583
When Vírka visited the Dead Sea, she took a bowl with sand, pebbles, and water from the sea as a souvenir. The water in the bowl weighed 400g. How many deciliters of water did the eddy carry away from the sea? The density of salt water in the Dead Sea is - The body
The body has a volume of 15 cubic centimeters and a weight of 117 grams. What is its density? - Diameter 30533
The open tank has the shape of a cylinder with a diameter of d = 1 m and a height of v = 2 m. How many m² of sheet metal is needed to make the tank? How many liters of water will fit in this tank? - Sphere parts, segment
A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. What are the volume of the segment and the surface of the segment?
- Density 30441
How many kg weighs 1 m³ of gold? Au gold density is 19.3 kg · dm − 3 - Hexagonal prism
Calculate the volume and surface of a regular hexagonal prism with the edge of the base a = 6 cm with the corresponding height v1 = 5.2cm and the height of the prism h = 1 dm. - Quadrilateral 30401
Calculate the volume of a regular quadrilateral pyramid, given: 1) a = 3.5 m; vt = 24 dm Express the volume in m³ and round to 1 decimal place 2) a = 1.6 dm; vt = 295 mm Calculate the volume in cm³ and round to 1 decimal place Solution entry: 1) entry 2) - Calculate 30391
Calculate a sphere's surface area and weight if its volume is 707.54 cm³ and if it is made of a material with a density of 7.8 g / cm³. - Cylinder-shaped 30381
Evelina wanted to pour 2 liters of lemonade into a cylinder-shaped glass with a bottom diameter of 5 cm and a height of 8 cm. What is the volume of the glass, and can 2dl of lemonade fit in it?
- Calculate 30361
Calculate the volume and surface of the cylinder r = 4cm, v = 6cm. - Sandbox
How many cubic meters of sand are needed to fill the sandbox on the field if it has the shape of a circle with a diameter of 3 m and is 25 cm deep? - Barrel-shaped 30341
The barrel-shaped barrel has a base diameter of 6 dm and a height of 1.2 m. How many 5-liter buckets will we fill it to 3/4 of its height? - The volume
The volume of the sphere is 1 m³. What is its surface? - Used cars
Peter plans to buy a used car: the first car Renault Espace 2.0 dCi 16V Dynamique 2006, costs 2000 euros. It is 14 years old and has a combined diesel consumption of 8 liters. / 100 km. Diesel costs 1.1 euros/liter. How much will the car cost him to opera
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