Practice problems of the volume - page 33 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
- Dredged 47291
The pit for the pool will be 30 meters long, 15 meters wide, and 2 meters deep. How many cubic meters of clay need to be dredged? - Cross-section 47131
The 5 m long bar has a cross-section of an equilateral triangle with a side of 35 mm. Calculate its volume - Picture 47121
A 25 cm high layer of snow fell on the garden 110 m long and 60 m wide. How many m³ of snow fell? Draw a picture. - Dimensions 47111
The block's dimensions are 9: 5: 4. Determine its volume if you know that the sum of the longest and shortest edges is 65 cm.
- Cylindrical 46983
62.8 hl of water per hour flows through the pipe into an empty cylindrical tank with a bottom diameter of 8 m. In 4 hours, the tank will be filled to what height? - Mr. Gardener
Mr. Gardener wants to make wood for the balcony. Boxes. Each will have the shape of a perpendicular prism with a square base. The height is limited to 60 cm. He will fill each container with soil by pouring the whole bag of substrate sold into a package c - Frustrum - volume, area
Calculate the surface and volume of a truncated rotating cone with base radii of 8 cm and 4 cm and a height of 5 cm. - Quarter-liter 46873
We filled half the jug with water. We poured this water into quarter-liter cups. Five cups filled to the brim, the sixth only half its volume. What is the volume of the pitcher? - Tower
Charles built a tower of cubes with an edge 2 cm long. In the lowest layer, there were six cubes (in one row) in six rows. In each subsequent layer, always one cube and one row less. What volume in cm³ did the whole tower have?
- Rectangle 46791
We rolled up the shell of a 4 cm high rotating cylinder from a rectangle measuring 6 cm and 4 cm. Find the volume of the cylinder. - Consecutive 46761
The block lengths are made up of three consecutive GP members. The sum of the lengths of all edges is 84 cm, and the volume block is 64 cm³. Determine the surface of the block. - Calculate 46741
Calculate the weight of the pendant - a regular four-side prism made of glass. The density of the glass is 2.5 g / cm3, the edge of the base is 2 cm, and the height of the pendant is 5.5 cm. - Contained 46731
The diesel tank has the shape of a block measuring 4.5 m x 3.2 m. What was the level of the diesel if it contained 216 hl of diesel? - Decorative 46721
How many liters of water can fit in a decorative garden tank in the shape of a regular hexagonal pyramid with a 30 cm long base edge? The depth of the tank is 30 cm.
- Regular quadrilateral pyramid
Find the surface area of a regular quadrilateral pyramid if for its volume V and body height v and the base edge a applies: V = 2.8 m³, v = 2.1 m - Diameter 46661
The granite ball has a diameter of 80 cm. The mass of 1m³ of granite is 2900 kg. What is the mass of the ball? - Triangular 46641
The regular triangular pyramid ABCDV has a base edge length of 8 cm and a height of 7 cm. Calculate the pyramid's surface area and volume. - Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1:3. Calculate the surface of the prism. - Increase 46473
He enlarges the side of the 8 cm long cube by 20%. How much will its volume increase compare to the original cube?
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