# Geometry + reason - math problems

#### Number of problems found: 61

- Tower

Charles built a tower of cubes with an edge 2 cm long. In the lowest layer there were 6 cubes (in one row) in six rows, in each subsequent layer always 1 cube and one row less. What volume in cm^{3}did the whole tower have? - Divide an isosceles triangle

How to divide an isosceles triangle into two parts with equal contents perpendicular to the axis of symmetry (into a trapezoid and a triangle)? - Metal balls

Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level? - 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? - 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? - Poplar shadow

The nine-meter poplar casts a shadow 16.2 m long. How long does a shadow cast by Peter at the same time, if it is 1.4 m high? - 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? - Candles

Before Christmas, Eva bought two cylindrical candles - red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 p. M. , lit a green candle at 7:00 p. M. , and left them both on fire until they burned. At 9:30 p. M. , bo - 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. - Integer cube

The length of the cube edge is an integer. Its volume is in cm^{3}a five-digit number divisible by 1331. What is the length of the edge of this cube. - Three parallels

The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - Coordinates of square vertices

I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C and D. Thanks, Peter. - Hexagon

Divide a regular hexagon into lines into nine completely identical parts; none of them must be in a mirror image (individual parts can only be rotated arbitrarily). - Set of coordinates

Consider the following ordered pairs that represent a relation. {(–4, –7), (0, 6), (5, –3), (5, 2)} What can be concluded of the domain and range for this relation? - Centroid - two bodies

A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi - 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). - Tangent spheres

A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and - Bricks pyramid

How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid? - Find the

Find the image A´ of point A [1,2] in axial symmetry with the axis p: x = -1 + 3t, y = -2 + t (t = are real number) - The publisher

The publisher prepares the release of the dictionary. Print preparation costs no matter the number of printed copies of 150000 CZK. The printer charges 80 CZK for one print. A) What are the costs of one dictionary if 5000 copies printed? B) For what numbe

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Geometry - math problems. Reason - math problems.