Geometry + cube - practice problems - last page
Number of problems found: 478
- Rectangle pool
Find dimensions of an open pool with a square bottom with a capacity of 32 m³ to have painted/bricked walls with the least amount of material. - Mountain 64314
The hiker set out on a hike at 5 km/h. After 30 minutes, a cyclist on a mountain bike set off on the same route at 20 km/h. How many minutes will the cyclist overtake the tourist? - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Kilograms 66864
The sculptor composes an ice city from ice cubes. The cube with an edge length of 2 dm weighs 7.2 kg. How many kilograms is an ice cube with an edge length of 6 dm heavier than it?
- Diagonals 3580
Cube edge length 5cm. Draw different diagonals. - Perfect cubes
Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube? - Weigh 8301
How much does a gold cube weigh, 30 x 30 x 30 cm? - Volume 33051
We have two cubes of the same weight. One is all made of glass, the other of cork. Which one has more volume, and how many times? - 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?
- Distribute 32451
The king cannot decide how to distribute 4 cubes of pure gold, which have edges of length 3cm, 4cm, 5cm, and 6cm, to two sons as fairly as possible. Design a solution so that the cubes do not have to be cut. - Perpendicular 5865
We cut the cube with two mutually perpendicular cuts, each parallel to one of the cube's walls. By what percentage is the sum of the surfaces of all cuboids created in this way greater than the surface of the original cube? - Eiffel Tower
Eiffel Tower in Paris is 300 meters high and is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material if it weighs 1.8 kg? - Definitely 83326
We roll the dice five times. Make sentences: a) 3 events that definitely cannot happen. Write a reason for each. b) 3 events that will definitely occur; write a reason for each. Another problem: 3 events that may or may not occur for each. Write a reason. - Seawater
Seawater density is 1025 kg/m³, and ice is 920 kg/m³. Eight liters of seawater froze and created a cube. Calculate the size of the cube edge.
- Shortest walk
An ant is crawling around this cube. The cube is made of wire. Each side of the cube is 3 inches long. (Those sides are called edges.) Points A and B are vertices of the cube. What is the least distance the ant would have to crawl if it starts from point - Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Cube - angles
Calculate the angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and the cube base. - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube.
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