Practice problems of the volume - page 45 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: 2353
- Two vases
Michaela has two vases in her collection. The first vase has the shape of a cone with a base diameter d = 20 cm; the second vase has the shape of a truncated cone with the lower base d1 = 25 cm and the diameter of the upper base d2 = 15 cm. Which vase can - Ball-shaped 32173
The inner diameter of the ball-shaped reservoir is d = 12 m. Can it hold 900 m³ of water? - Cross-section 32163
The bottom of the garden pool of circular cross-section has an inner diameter of d = 4 m. The water depth is 0.8 m. How many liters of water can we fill into the pool? - Cuboid diagonals
The cuboid has dimensions of 15, 20, and 40 cm. Calculate its volume and surface, the length of the body diagonal, and the lengths of all three wall diagonals.
- Calculate 32133
The cube has an area of 486 dm². Calculate the length of its side, its volume, the length of the body, and wall diagonals. - Aquarium
How many liters of water can fit in an aquarium measuring 30, 15, and 20 cm? - Calculate 32001
Calculate the volume of a 1.4 m high hexagonal prism container with a base area of 8300 cm². - Calculate 31991
Calculate the volume and surface of a prism whose height is 16 cm, and the base is in the shape of a right triangle with 5cm and 12cm trunks and a 13cm diaphragm. - Three-quarters 31981
The oil tank is shaped like a cylinder with a height of 8 m and a diameter of 4 m. It is three-quarters full. How much oil is in it?
- Children's 31961
The pool for swimmers has dimensions of 25m, 10m, and 2.8m, and the children's pool is only 10m, 4m, and 1m. The pump will change all the water in the swimming pool in 9 hours. How long does it take for the same pump to pump out the water in the children' - Calculated 31901
The company is to dig a well 25 m deep with a radius of 0.8 m. How many cars that can be loaded with 12 cubic m will be needed to transport the excavated soil if it is calculated that the soil will increase in volume by 10% when excavated? - Regular quadrilateral pyramid
Find the surface area of a regular quadrilateral pyramid with a volume of 24 dm³ and a height of 45 cm. - Dimensions 31751
The freezer box has internal dimensions of 900 mm, 0.75 m, and 6 dm. 30% of the space is filled with frozen peppers packed in boxes measuring 150mm, 100mm, and 50mm. How many boxes are in the box? - Ice floe
What is the volume of an ice floe weighing 326 kg? The density of ice is only 920 kg/m³.
- Dimensions 31681
The welded sheet metal tub is shaped a prism with dimensions of 6x2x2 m. How many m³ of water can fit in it, and what is its surface? - Bottles 31621
We filled 90 liters of must into bottles. Some have a volume of 1 liter, and some with a volume of 1.5 liters. We have a total of 70 bottles of must. How many bottles of each species did we fill? - Half-cylinder-shaped 31491
How many cubic meters of air is in an empty half-cylinder-shaped aircraft hangar if the hall is 30 m long and 12 m high at the highest point? - The body
The body has 2 m, 2 dm, and 10 cm dimensions. It weighs 28 kg. What is its density? - Cube edges
The cube has an edge of 4 cm. It has the same volume as a block, the base of which has an area of 32 cm². What height is the block?
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