# Geometry - math word problems

#### Number of problems found: 1491

- Circle

Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: (x-x_S)^{2}+(y-y_S)^{2}=r^{2} - Triangular prism

The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - Truncated pyramid

Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm. - Mast shadow

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines. - Pillar

Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48. - Crossroads

A passenger car and an ambulance come to the rectangular crossroad, the ambulance left. Passenger car at speed 39 km/h and ambulance at 41 km/h. Calculate such a relative speed of the ambulance move to the car. - How many

How many m^{2}of copper sheet is needed to replace the roof of a conical tower with a diameter of 13 meters and a height of 24 meters if we count 8% of the material for bending and waste? - Two chords

There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure. - Construct

Construct a rhombus ABCD with side a = 7cm, b = 5cm, whose diagonal e is perpendicular to side b. - Tower's view

From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church. - Water container

The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container? - MO - triangles

On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg - Length of the chord

Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°. - Triangle SSA

Construct a triangle ABC if |AB| = 5cm v_{a}= 3cm, CAB = 50 °. It is to create the analysis and construction steps. - Two bodies

The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco - Iceberg

What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg? - Cylinder

In a 1-meter diameter cylinder is 1413 liters of water, which is 60% of the cylinder. Calculate the cylinder height in meters, do not write the units. The resulting value round and write as an integer. - Twice of radius

How many times does the surface of a sphere decrease if we reduce its radius twice? - Hexagon - MO

The picture shows the ABCD square, the EFGD square and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ| - Largest possible cone

It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, 7.2 cm. a) Calculate its volume. b) Calculate the waste.

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