Practice problems of the volume - page 56 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
- Cone from cube
From a wooden block, 20 cm high was the turned largest possible cone. Calculate its weight if you know that the density of wood was 850 kg/m³ - Rain
Garden shape of a rectangle measuring 15 m and 20 m rained water up to 3 mm. How many liters of water rained in the garden? - Cannonballs
Three cannonballs with a diameter of 16 cm landed in the castle courtyard during the battle. The castle blacksmith made balls with a diameter of 10 cm, which fit into the cannons placed on the walls. How many cannonballs did the blacksmith cast? - Diameter = height
The cylinder's surface, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
- The Earth
The Earth's surface is 510,000,000 km². Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere. - Calculate 21743
Calculate the volume of the block in liters with edge lengths of 3dm, 15cm, and 120mm. - Circumference 21603
The circumference of the diamond is 29.6dm. a - calculate the length of its side b - calculate the area of the diamond if its height measures 5 dm - Quadrilateral 21523
Calculate the surface area and volume of a regular quadrilateral pyramid if the edge of the lower base is 18 cm and the edge of the upper base is 15 cm. The wall height is 9 cm. - Embankment
The railway embankment 300 m long has a cross-section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m³ of soil is in the embankment.
- Block-shaped 21493
How many sheets need to be closed on the block-shaped container above), which is 4 m wide, 250 cm long, and 35 dm high? How many liters of water can fit in it? - Perpendicular 21433
Calculate the height of the vertical prism with the rectangle's base if the dimensions of the edges of the floor are a = 12 dm, b = 50 mm, and the prism's volume V = 0.6 l. - Spherical 21373
The spoon has the shape of half a spherical surface with a radius of 50 mm. What volume of fluid does it fit when filled to the brim? - Cylinder-shaped 21363
82 hl of water per hour flows into the empty cylinder-shaped pool with a bottom diameter of 7.5 m. How high will the pool be filled if the water has flowed in for 4 hours? - Water mixing
There are 5 liters of water at 75°C in the pot. How much water at 10°C do we have to add to the resulting temperature of 55°C?
- The copper wire
The copper wire bundle with a diameter of 2.8mm weighs 5kg. How many meters of wire are bundled if 1m³ of copper weighs 8930kg? - Centimeters 21193
What is the height of a block whose base edges are 12 centimeters long and 6 centimeters long if its volume is 360 cubic centimeters? - Diameter 21173
The water ball has a volume of 32,500m². How big is its diameter? - Calculate 21163
Calculate the volume and surface area of the sphere if given r = 36mm - Cylindrical 21123
When the body was immersed in a cylindrical vessel filled with water, the water level in the vessel rose by 28 mm. Calculate the volume of the immersed body if you know that the diameter of the bottom of the container is 8 cm.
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