Practice problems of the volume - page 117 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: 2351
- Sphere slices
Calculate the volume and surface of a sphere if the radii of a parallel cut r1=32 cm, r2=47 cm, and its distance v=21 cm. - Diamond
Find the side of the diamond if its area is S = 490 cm² and one diagonal u2 = 39 cm. - Lead cube
Calculate the cube's edge made from lead, which weighs 19 kg. The density of lead is 11341 kg/m³. - Cone and cube
About what percentage has cone with base radius r larger volume than a same high cube with square base with edge length r?
- Pump
What power does a pump output to move 4853 hl of water to a height of 31 m for 8 hours? - Truncated cone
Calculate the volume of a truncated cone with base radiuses r1=13 cm, r2 = 10 cm, and height v = 8 cm. - Copper sheet
The copper plate has a length of 2.2 m, width 92 cm, and weighs 5.6 kg. What is the plate thickness if 1 m³ weighs 8732 kg? - Cylinder
Calculate the dimensions of rotating cylindrical containers with volume 2 l if the container's height equals the base's diameter. - Car range
Kia has an average diesel consumption of 5 liters per 100 kilometers. What is the range of the car for 135 euros if fuel costs 1.4 EUR/liter, if the tank has a volume of 51 liters?
- Fuel consumption
Mazda car has an average nafty consumption of 4.2 liters per 100 kilometers. What is the car range for a full tank of volume 73 liters? - Wood in the forest
The amount of wood in the forest was estimated at 6000 m³. How much wood will be in the forest after 2 years if the annual growth of wood is 2.5% each year and logging 30 m³ each year? - Air mass
What is the weight of the air in a classroom with dimensions 10 m × 10 m × 2.7 m? The air density is 1.293 kg/m³. - Solid in water
The solid weighs in air 16.1 kg and in water 13 kg. Calculate the density of the solid. - Barrel of oil
The barrel of oil weighs 283 kg. When it molded 26% oil, it weighed 216 kg. What is the mass of the empty barrel?
- Cylinder - basics
Cylinder with base radius r = 54 cm and height h=35 cm. Calculate: a) Area of the base - Cylinder - A&V
The cylinder has a volume of 463. The base has a radius 4. What is the area of the surface of the cylinder? - Sphere A2V
The surface of the sphere is 241 mm². What is its volume? - Sphere fall
How much percent fall volume of a sphere if diameter decreases 3×? - Sphere growth
How many times does a volume of the sphere rise if diameter rises 10×?
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