Practice problems of the volume - page 49 of 117
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: 2323
- The quadrilateral pyramid
The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area. - Swimming pool
The swimming pool has the shape of a block with dimensions of 70dm, 25m, and 200cm. How many hectoliters of water can fit into the pool? - The tax
The tax per gallon of gasoline in California is $0.477. If you fill your gasoline tank with 14.4 gallons in California, how much will you pay in taxes? Round to the nearest cent. - Water level
How many cm will the water level in a cube-shaped tank with an edge of 3 m drop if we discharge 189 hl of water? - Iron ball
The iron ball weighs 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm³. - Caleb
Caleb is making lemonade for a party. He has 5 gallons of lemonade. He puts 1/3 cubic inch of lemonade in a cup for each guest. How many guests are going to be at the party? - Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Base of house
Calculate the volume of the bases of a square house. If the base depth is 1.2 m, the width is 40 cm, and their outer circumference is 40.7 m. - A regular
A regular triangular prism with a base edge of 20 dm and a height of 30 dm is drawn. Find the volume of the prism and the area of the shell. - Granite cube statue
What is the weight of a granite cube with an edge length of 75 cm if one m³ of granite weighs 2.7 tons? - Rain
It rains at night. On 1 m² of the lake will drop 60 liters of water. How many cm will the lake level rise? - Triangular prism
Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height) - Cube corners
We cut a small cube with an edge length of 2 cm from each corner of a large cube with an edge length of 10 cm. How many cm³ was the body left from the big cube after cutting the small cubes? - The cast
The cast in the body of a regular quadrilateral pyramid with a base edge 60 cm long and 5 cm high is made of a material with a density of 7.8 g/cm cubic. Calculate its weight. - Triangular prism
The perpendicular triangular prism is a right triangle with a 5 cm leg. The prism's largest wall area is 130 cm2, and the body height is 10 cm. Calculate the body volume. - 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. - Tank
To cuboid tank whose bottom has dimensions of 9 m and 15 m were flow 1080 hectoliters of water. This filled 40% of the tank volume. Calculate the depth of the tank. - Alcohol
How many cubic centimeters of 96% alcohol is needed to obtain 0.75 liters of 40% alcohol? - Digging
A pit is dug in the shape of a cuboid with dimensions 10mX8mX3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions of 40m X 30m. What is the increase in the level of the plot? - Two pipes
One pipe fills one-fifth volume 20 minutes before my second one. The two pipes together will fill the tank in two hours. How long will fill the tank of each pipe separately?
Do you have homework that you need help solving? Ask a question, and we will try to solve it.