Geometry - math word problems
Number of problems found: 1526
- 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
- Earth parallel
Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
- Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
The car runs on a horizontal track at a constant speed of 20 m2-1. It is raining. Raindrops fall in a vertical direction at a speed of 6 m/s. a) How fast is the speed of the drops relative to the car windows? b) What is the angle of the raindro
- Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
Cylinder was drawn in scale 2:1. How many times is the volume of the cylinder smaller in reality?
- Tangents to ellipse
Find the magnitude of the angle at which the ellipse x² + 5 y² = 5 is visible from the point P[5, 1].
Pyramid has a base a = 3cm and height in v = 15 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1°
- Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
Calculate the angle between box base 9 x 14 and body diagonal length 18.
- Cube - angles
Calculate the angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
- Inclined plane
The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body.
- Rotary cone
The volume of the rotation of the cone is 472 cm3, and the angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone.
- What percentage
What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
- Pentagonal pyramid
Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
- Resultant force
Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
- Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
- Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%.
- Cone side
Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.