Solid geometry, stereometry - page 32 of 123
Number of problems found: 2441
- An example
An example is playfully for grade 6 from Math, and I don't know how to explain it to my daughter when I don't want to use the calculator to calculate the cube root. Thus: The student made a cuboid from a block of 16x18x48 mm of plasticine. What will be th - Cube-shaped box
Find the size of the smallest possible cube-shaped box where three types of 3cm, 5cm, and 6cm small cubes could be stacked to fully use the box space (each type of cube separately). Can you find out how many smallest cubes are in the box? - A residential
A residential colony has a population of 5400, and 60 liters of water is required per person per day. The effective utilization of rainwater constructed a water reservoir measuring 48m × 27m × 25m to collect the rainwater. For how many days is the water i - Cube-shaped container
The cube-shaped container has a height of 52 cm and a square base. The container was filled to the brim with water, and then we immersed a metal cube in it, which caused 2.7 l of water to flow out of the container. After removing the cube from the water, - Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm³. - For thinkings
The glass cube dives into the aquarium, which has a length of 25 cm, a width of 20 cm, and a height of 30 cm. Aquarium water rises by 2 cm. a) What is the volume of a cube? b) How many centimeters measure its edge? - Identical cubes
From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12 dm x 16 dm x 20 dm? - Chocolate ball comparison
What should a sweet tooth choose if he wants more chocolate: a package containing 200 pieces of solid chocolate balls with a diameter of 1 centimeter or a hollow ball with an outer diameter of 10 cm made of 5 mm thick chocolate? - Two boxes-cubes
Two boxes of a cube with edges a=28 cm and b = 92 cm are to be replaced by one cube-shaped box (same overall volume). How long will its edge be? - Two rectangular boxes
Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and second of 5 cm, 12 cm, and 1 dm will be replaced by a single cube box of the same cubic volume. Calculate its surface. - Rainfall
A rectangular garden of 25m in length and width 20m in width is filled with 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water. - Cube building blocks
Little Paul was assembling building blocks (a cube is shaped like a cube). He wanted to build a big cube. However, he had 75 dice left, so he increased the edge by one die. Then he was missing 16 dice. How many cubes did he have in the kit? - Volume per time
The length of the cube-shaped tank edge is 4 m. A pump has a capacity of 200 l per minute. How long does it take for a pump to fill a cube-shaped tank up to 75% of its height? - Steel ball radius
Twenty identical steel balls were dropped into a cylindrical container of water standing on a horizontal surface to submerge them below the surface. At the same time, the water level rose by 4 mm. Determine the radius of one sphere if the diameter of the - Wooden ball diameter
A solid wooden ball made of beech wood weighs 800 g. Calculate its diameter if the wood density is ρ = 750 kg/m³ - Ice Cube Edge Length
The ice cube weighs 24g. Determine the size of its edge to the nearest millimeter. If the ice density is 917kg/m3 - Small and big box
Boxes with dimensions of 6 cm, 10 cm, and 15 cm should fit into a cube-shaped box. What are the smallest dimensions a box can have? How many boxes of the given dimensions can fit in it? - Iron sphere
Iron sphere weights 100 kg and density ρ = 7600 kg/m³. Calculate the volume, surface, and diameter of the sphere. - The solar
The solar heating tank has the shape of a rotating cylinder. When the tank is in a horizontal position, the water in the tank wets 4/5 of each tank base. If we place the tank in a vertical position, the water in the tank will reach up to 1.2 m. Calculate - Large Cube Surface
Fifty small metal cubes with an edge length of 2 cm were deformed, and we made one large cube from this material. What is its surface?
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