Geometry - math word problems - page 159 of 165
Number of problems found: 3289
- Vector sum
The magnitude of the vector u is 2 and the magnitude of the vector v is 11. The angle between vectors is 64°. What is the magnitude of the vector u + v? - Vectors
Find the magnitude of the angle between two vectors u = (3; -5) and v = (10; 6) - Circular pool
The pool's base is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length of 10 meters. The pool depth is h = 2 m. How many hectoliters of water can fit into the pool? - The angle of lines
Calculate the angle between the two lines y = x-8 and y = +12. - Flowerbed
The flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be pl - Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides are consecutive terms of an arithmetic progression. - Raindrops
The train is moving at a speed of 60 km/h. Raindrops falling vertically in the absence of wind (with uniform movement due to the action of air resistance) leave traces on the windows of the train, deviating from the vertical direction by 30°. How fast are - Base RR odd
The base of a prism is an isosceles trapezoid ABCD with bases AB = 12 cm and CD = 9 cm. The angle at vertex B is 48°10′. Determine the volume and surface area of the prism if its height is 35 cm. - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and whose body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Tetrahedral pyramid 8
Let all the side edges of the tetrahedral pyramid ABCDV be equally long and its base let us be a rectangle. Find its volume if you know the deviations A=52° B=56° between the planes of adjacent sidewalls and the base plane. The height of the pyramid is h= - Cross-section of a roof
The owner must cover the carport with a hipped roof with a rectangular cross-section of 8 m x 5 m. All roof surfaces have the same slope of 30°. Determine the price and weight of the roof if 1 m² cost €270 and weighs 43 kg. - The cone
The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane. (The cone side is the segment joining the vertex cone with any point of the base circle. All sides - Angle between lines
Calculate the angle between the following two lines: p: -4x +7y +7 =0 q: -x +4y +7=0 - Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1 m 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 grav - Eight blocks
Dana had the task of saving the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be fo - Tower
How many m² of the copper plate should be replaced on the roof of the conical tower shape with a diameter 23 m, and the angle at the axial section's vertex is 119°? - The spacecraft
The spacecraft spotted a radar device at an altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615 km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is consider - Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 30 degrees, |AB| = 15 cm. Calculate the volume of the prism. - An Elizabethan collar
An Elizabethan collar is used to prevent an animal from irritating a wound. The angle between the opening (diameter 6 inches) with a 16-inch diameter and the side of the collar is 53 degrees. Find the surface area of the collar shown. - Decagon prism
A regular decagon of side a = 2 cm is the base of the perpendicular prism. The side walls are squares. Find the prism volume in cm³, round to two decimal places.
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