# Length + expression of a variable from the formula - math problems

- Cutting cone

A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - Circle and square

An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD. - Observation tower

From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower? - Wire fence

The wire fence around the garden is 160 m long. One side of the garden is three times longer than the other. How many meters do the individual sides of the garden measure? - A map

A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field? - Two rectangular boxes

Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface. - Squares ratio

The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte - A cell tower

A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal? - Triangular pyramid

A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm - The quadrilateral pyramid

The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area. - Rotaty motion

What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling? - The perimeter of the rectangle

The length, l, of a rectangle is 4 inches greater than its width, w. The perimeter of the rectangle is at least 30 inches. What inequality shows the range of possible widths of the rectangle? - Rectangle field

The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m? - A rhombus

A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus. - Tetrahedral pyramid

A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area). - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Radius of the circle

Calculate the radius of the circle whose length is 107 cm larger than its diameter - The Eiffel Tower

The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height. - Wooden container

The cube-shaped wooden container should be covered with a metal sheet inside. The outer edge of the container is 54cm. The wall thickness is 25 mm. The container has no lid. Calculate. How many sheets will be needed to cover it? - Three altitudes

A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.

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