# Geometry + reason - practice problems

#### Number of problems found: 62

- Water container

Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container? - The body

The body on the figure consists of cubes with an edge length 10 cm. What surface has this body? - Lines

How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line? - Points in plane

The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points? - Ribbon on the cube

A cubical gift box is tied with a piece of ribbon. If the total length of the free ends and the bow is 18 inches, what is the length of the ribbon used? (Each side of the cube is 6 inches). - 2d shape

Calculate the content of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of the segment AB is 5 cm. - Barrel 3

Barrel with water weights 118 kg. When we get off 75% of water, it weights 35 kg. How many kg has an empty barrel? - Hexagon rotation

A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - No smoke

Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with the cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. The regular cigarette contains 0.8 mg of nicotine. How much nicotine would a gian - Dodecagon

Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - 2x cone

Circular cone height 84 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone. - Spheres in sphere

How many spheres with a radius of 15 cm can fit into the larger sphere with a radius of 150 cm? - A cylinder

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the top and bottom. (forming a spiral around the cylinder). How long is the string in cm? - Sphere cut

A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center of the sphere? - Cuboid and ratio

Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid. - Integer cube

The length of the cube edge is an integer. Its volume is in cm³ a five-digit number divisible by 1331. What is the length of the edge of this cube. - Points in space

There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - Painting

To paint the pool with dimensions: 2 meters depth, 3m x 4m we bought paint to 50 meters square. How many "paint" will be a waste? - Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE is divided into a triangle and parallelogram, as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE, and the area of the triangle CDE is 3 cm². Determine the area of the trape - 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?

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Geometry - practice problems. Reason - practice problems.