System of equations + volume - practice problems - page 2 of 6
Number of problems found: 101
- The cylinder
In a rotating cylinder, it is given: the surface of the shell (without bases) S = 96 cm² and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder. - Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height. - Consecutive members
The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, and c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence. - Calculate 33911
Calculate the volume of 50% KI solution and the volume of 20% KI solution needed to prepare 180g of 30% KI solution. The solution densities are known: ρ50% = 1.54575 g / cm3, ρ20% = 1.16597 g / cm³. - Fresh juice
The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him. A liter of juice costs 40 CZK more than a bottle. There is no charge for turning the juice - Bottles 31621
We filled 90 liters of must into bottles. Some have a volume of 1 liter, and some with a volume of 1.5 liters. We have a total of 70 bottles of must. How many bottles of each species did we fill? - The water barrel
The water barrel weighs 122 kg. If we pour 75% of the water out of it, it will weigh 35 kg. What is the weight of the barrel? - Reservoirs 29051
The three water reservoirs hold a total of 130 liters. Determine their volumes in m³. If the first fits 15 liters less than the second and 20 liters less than the third. - Manufacturing 28591
A furniture manufacturing company consumes 124 cubic meters of spruce and oak lumber per month. Spruce lumber consumes three times more than oak lumber. How much spruce and oak lumber does the company use per month? - A bottle
A bottle full of cola weighs 1,320 g. If we drink three-tenths of it, it will weigh 1,008g. How much does an empty bottle weigh? - Water mixing
We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C? - In the dairy
There were three times more milk packages in the dairy than half a liter. Four times more liters remained when sold in 10 liters and ten half-liter containers than in half-liter packages. How many packages were there originally? - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - Concentration 17633
If we mix 4l and 6l of differently concentrated salt solutions, we get a 12% solution. If we use 6l of the first and 4l of the second solution, we get a 13% solution. What is the concentration of each solution? - Wines
Eleven liters of white wine and eight liters of red wine cost a total of 1315 CZK. 1 liter of white wine was 10 CZK cheaper than a liter of red wine. How much is 1 liter of white and how much red wine? - Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - Milk
There were 22 liters of milk in three containers. There were 6 liters more in the first container than in the second. After pouring 5 liters from the first container into the third container, the same quantity of milk is in the second and third containers - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Dividing money
Vilem, Cenek, and Edita divided the money they earned by spreading the leaflet. Vilem got 240 CZK more than Cenek and twice more than Edita. Edita got 400kc less than Vilem. How much did each of them earn? - Camel and water
84% of the camel's weight is water. After drinking, its weight increased to 832 kg, and water accounted for 85% of its weight. How much did it weigh before drinking?
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