Practice problems of the volume - page 97 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
- 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. - Two-thirds 3388
The kneaded cake dough has a volume of 1.8 l. When baking, it increases its volume by about two-thirds. Can a baked wheel fit on a baking sheet measuring 36x30x8cm? How tall will the cake be after baking? - Consumption 3385
A liter of gasoline costs 1.516 euros. The average consumption of the KOLO car is 6.9 l per hundred kilometers. The car has a 40-liter tank. How much will the car owner pay for the trip from Zilina to Prague and back if he follows the 413km long route?
- Hectoliters 3382
288 hectoliters of water were in the block tank. The tank has dimensions of the bottom 12m and 6m and a depth of 2m. What percent of the tank volume does the water occupy? - Quarter-liter 3380
A container has the shape of a regular hexagonal prism with a base with a capacity of 0.5dm2, which three quarter-liter cups of water fill to the brim. What is the height of a container? - Cuboid and ratio
A cuboid has dimensions in a ratio of 1:2:6, and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid. - Cone
The rotating cone volume is 9.42 cm3, with a height of 10 cm. What angle is between the side of the cone and its base? - Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
- Circumference 3370
Calculate the surface and volume of the rotating cone, whose base circumference is 125.6 cm and the side is 25 cm long. - Cylinder-shaped 3368
The cylinder-shaped silo (d = 2.8 m and v = 9 m) is 65% filled. How much silage can we store in it? - Cylindrical tank
The cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder. - Height 3344
The bottom is 25m wide and 10m long, and there is 37640 hl of water. What height does the water reach? - Hectoliters 3342
We filled the water tank from 3/5 of its volume. After releasing 21 hl, only 1/4 of the entire volume remained. How many hectoliters of water can the tank hold?
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