Solid geometry + cube - practice problems
Number of problems found: 231
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
One cube has an edge increased five times. How many times will larger it's surface area and volume?
How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds?
- Into box
How many cubes with an edge of 2.5 cm fit into a box measuring 11.6 cm; 8.9 cm and 13.75 cm?
- Surface area 2
Calculate how many % reduce the surface area of the cube is we reduced length of each edge by 10%.
- Reduce of the volume
Calculate how many % reduce the volume of the cube is we reduced length of each edge by 10%.
- Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the volume of the cube from the volume of the ball?
- Minimum surface
Find the length, breadth, and height of the cuboid-shaped box with a minimum surface area, into which 50 cuboid-shaped blocks, each with length, breadth, and height equal to 4 cm, 3 cm, and 2 cm respectively, can be packed.
- Prism bases
Volume perpendicular quadrilateral prism is 360 cm³. The edges of the base and height of the prism are in the ratio 5:4:2. Determine the area of the base and walls of the prism.
- Granite cube statue
What is the weight of a granite cube with an edge length of 75 cm, if 1 m³ of granite has a weight of 2.7 tons?
- Inscribed sphere
How many percent of the cube volume takes the sphere inscribed into it?
- Cube in ball
Cube is inscribed into the sphere of radius 181 dm. How many percent is the volume of cube of the volume of the sphere?
- Cube construction
A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
- Cuboid and ratio
Find the dimensions of a cuboid having a volume of 810 cm³ if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
- Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
- The wooden
The wooden block measures 12 cm, 24 cm, and 30 cm. Peter wants to cut it into several identical cubes. At least how many cubes can he get?
- Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
- Transforming cuboid
Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
Brass is an alloy of copper and zinc. The 10 centimeter brass cube has a weight of 8.6 kg. Copper density is 8930 kg/m3, the zinc density is 7130 kg/m³. Calculate how many kg of copper and zinc a cube contains.
- Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
Solid geometry, stereometry. Cube practice problems.