Practice problems of the volume - page 116 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
- Cone
The circular cone has height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane if solids have the same volume. - Pool
If water flows into the pool by two inlets, fill the whole for 20 hours. The first inlet filled the pool 8 hour longer than the second. How long does the pool take to fill with two inlets separately? - Cube
The cube weighs 11 kg. How weight is a cube of the same material if its dimensions are 3-times smaller? - Water
Into a full cylindrical tank high 3 m with a base radius of 2.5 m, we insert a cuboid with dimensions 1.7 m, 1.3 m, 1.9 m. How many liters of water will overflow out?
- Cube corners
From the cube of edge 5 cm, we cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will this body have? - Sea on the Moon
Assume that the Moon has a sea with the same composition as Earth's (it has the same density of saltwater). Calculate the boat's dive floating in the sea on the Moon when on Earth has dive 3.9 m. Consider that the Moon has 6.5-times smaller gravitational - Cube corners
Peter cut the wooden cube with edge 64 cm in 3 corners of the cube with edge 4 cm. How many cubes of edge 4 cm can Peter even be cut? - Hole
They fill the shape hole with dimensions 2.9 m, 17 m, 15.2 m with 97 m³ of soil. How much percent does it fill up? - Cubic
Convert 660 m³ of natural gas volume to energy units kWh. Combustion of 1 cubic meter of natural gas is released energy 10.55 kWh.
- Sphere
The sphere's surface is 12100 cm², and the weight is 136 kg. What is its density? - Shots
5500 lead shots with diameter 4 mm are decanted into a ball. What is its diameter? - Bricks
Brick has volume 2.4 dm³. How many bricks can drive a truck with a capacity of 15 ton? The density of brick is 2 g/cm³. - Rainfall
Annual rainfall in our country is an average of 797 mm. How many m³ of water rains on average per hectare? - Special cube
Calculate the cube's edge if its surface and volume are numerically equal numbers.
- Cube
The sum of lengths of cube edges is 56 cm. What are its surface and volume? - Transforming cuboid
A cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length? - Pipes
The water pipe has a cross-section 1184 cm². An hour has passed 743 m³ of water. How much water flows through the pipe with cross-section 300 cm² per 6 hours if water flows at the same speed? - Rotating cone
Calculate the volume of a rotating cone with base radius r=$r cm and height h=$v cm. - Gold wire
From one gram of gold was pulled wire 1.4 km length. What is its diameter if the density of Au is ρ=19.5 g/cm³?
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