Geometry - math word problems
Number of problems found: 1491
Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
- Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is from interval <0,1>.
- Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm3. Determine the length of the edges of a cube.
- Earth rotation
How fast is the place on the Earth's equator moving if the Earth's radius is 6378 km?
- Hollow sphere
The steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and the density of steel is 7850 kg/m3
- Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
- Vertex points
Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area.
- As shown
As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE
- Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
- The coil
How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
- Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, and its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
- Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
The trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
Draw a square ABCD whose diagonals have a length of 6 cm
- Find x 2
Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100. Write down the number of solutions.
- Construction of trapezoid
Construct a trapezoid if b = 4cm, c = 7cm, d = 4,5cm, v = 3 cm (Procedure, discussion, sketch, analysis, construction)
- 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.
- Iron density
Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
- Brass sphere
Find the weight of a brass ball with an outer radius of 12 cm, a wall thickness of 20 mm if the brass's density is 8.5 g/cm3.
- 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?