Practice problems of the volume - page 31 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: 2346
- Dynamometer
What is the volume of a body that stretches a dynamometer in air, on which a force of 2.5 N suspends it, and if it is immersed in alcohol with a density of 800 kg/m³, does it tension the dynamometer with a force of 1.3 N? - Ali bought
Ali bought 5/6 liters of milk. He drank 1/2 liter, and his brother drank 1/6 liter. How many liters of milk are left? - Luke
Luke, Seth, and Anja have empty glasses. Mr. Gabel pours 3/6 cups of orange juice into Seth's glass. Then he pouts 1/6 cup of orange juice in Luke's glass and 2/6 cup of orange juice in Anja's glass. Who gets the MOST orange juice? - Monica’s
Monica's lawnmower had 1/8 of a gallon of gasoline in the tank. Monica started mowing and used all of the gasoline. She put 6/10 of a gallon of gasoline in the tank. After she mowed, 1/4 of a gallon was left in the tank. What was the total amount of gasol - Imagine 2
Imagine that you are filling treat bags with jellybeans. You have 3 3/8 cups of jellybeans, and each treat bag will contain 1/4 cup of jellybeans. How many treat bags can you fill before you run out of jellybeans? Show your work (please). - The pool
There is 210 l of water in the pool. If you know that the pool is 30% full, calculate how many liters of water will fit into it. - Edges of the cuboid
Find the length of the edges of the cuboid, which has the following dimensions: width is 0.4 m; height is 5.8 dm, and the block can hold 81.2 liters of fluid. - The surface
The surface of the cylinder is 1570 cm²; its height is 15 cm. Find the volume and radius of the base. - Above water surface
If we remove the stone from the water, we apply a force of 120N. How much force will we exert if we move the stone above the water? The stone's density is 5000 kg/m³. - What power
What power should the radiator have in a room 5x4 meters with a height of 3 meters? Hint: Calculate 35 watts per meter³ when you need 22 degrees in the room, but you need about 24 degrees in the bathroom. It's an old heating cheat, but it will help you. - Hectoliters 48941
The pool has dimensions: a length of 50 m, a width of 15 m, and a depth of 2 m. It is filled with water to 1/4 of its depth. How many hectoliters of water are in the pool? How many hectoliters of water can fit in a filled pool? - Kenneth
Kenneth is painting his kitchen and bathroom. He bought 5 gallons of paint to paint the two rooms. He uses 1/4 of that amount to paint the bathroom and the rest from painting the kitchen. How many gallons of paint did Kenneth use to paint the kitchen? - There
There is 5 l of water with a temperature of 20°C in the bucket. We add 3 liters of hot water. The resulting temperature will be 30°C. What was the temperature of the hot water? - Dana and sandbox
Dana helped her dad build a sandbox for her younger sister. The sandbox is shaped like a rectangular prism, 4 1/2 feet long and 4 feet wide. Dana used bags of sand to fill the sandbox 1/2 of a foot deep. Each bag contained 1/2 of a cubic foot of sand. How - Feed to hay
How many tons of water do we have to dehydrate from 8 tons of feed if the original moisture is 54 percent to get hay with a moisture content of 15 percent? Round to two decimal places. - Cathy
Cathy has 5 cups of peanuts to share with her family. If each family member gets 1/2 cup of peanuts, how many family members can have some? - One-third 48373
40 g of washing powder is needed for 10 l of water. When washing in hard water, the dosage should be increased by one-third. How many grams of detergent is required per 10 liters of hard water? - Fruit punch
Kelly made fruit punch to serve at a party for her chess team. She mixed 1 2/5 liters of cranberry juice and 1 3/5 liters of pineapple juice together. Then, she split the fruit punch evenly among nine glasses. How much fruit punch did Kelly pour into ea - School model
The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm³ - Percentage 48223
The safe is 100 cm high, 80 cm wide, and 60 cm deep. Its internal space has a volume of 168 liters. What percentage of the total volume of the safe is occupied by the walls of the safe?
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