Practice problems of the volume - page 96 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: 2345
- Pyramid in cube
In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid. - The tent
The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m² of cloth did we need to make the tent if we have to add 7% of the seams? How many m³ of air will be in the tent? - Cube walls
Find the volume and surface area of the cube if the area of one wall is 40 cm². - Quadrangular prism
The regular quadrangular prism has a base edge of 7.1 cm and a side edge of 18.2 cm long. Calculate its volume and surface area. - Rotary bodies
The rotating cone and the rotary cylinder have the same volume of 180 cm³ and the same height, v = 15 cm. Which of these two bodies has a larger surface area? - Five pumps
Three same pumps fill the tank with 50400 liters of diesel in 7 hours. How many liters of diesel will it take in 4 hours if we add two more of the same pumps and pump them the same way? How much more (or less) will they get if we add 2 of the same pumps a - Copper wire
What is the weight of 1000 m copper wire with a diameter of 5 mm when metric density p = 8.8 g/cm³? - Aquarium 3432
The aquarium has the shape of a block with a length of 0.7 m and a width of 25 cm. It can hold 56 liters of water. How deep is the aquarium? - Inscribed sphere
How much % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube? - Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm. - Dimensions 3406
We poured 3 liters of water into an empty aquarium, with a bottom dimension of 30x30cm and a height of 25cm. What is the level? - Axial cut
The cone surface is 388.84 cm2, and the axial cut is an equilateral triangle. Find the cone volume. - Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the pyramid's height is 7 cm. - Support colum
Calculate the support column's volume and surface, which is shaped as a vertical quadrangular prism whose base is a rhombus with diagonals u1 = 102 cm and u2 = 64 cm. Column height is 1. 5m. - Traffic cones
Forty identical traffic cones with a base diameter d = 3 dm and a height v = 6 dm should be painted on the outside with orange paint (without base). How many crowns do we pay for color? If we need 50 cm³ of paint to paint, 1m² and 1l of paint cost CZK 80? - Roof 8
How many liters of air is under the tower's roof, which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof. - Cylindrical 3395
The cylindrical vase is 28 cm high. Its inner diameter d = 1.1 dm. How many liters of water will fit in it if the bottom thickness is 1.5 cm? - Cylindrical 3394
The cylindrical container with a diameter of 1.8 m contains 2000 l of water. What height does the water reach? - Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm. - Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
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