Geometry - math word problems - page 160 of 162

Number of problems found: 3232

Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism?
The roof
The tower's roof has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long, and the side wall of the animal with the base at an angle of 57°. Calculate how much roofing we need to cover the entire roof if we count on 15% waste.
Regular quadrangular pyramid
The height of the regular quadrangular pyramid is 6 cm, and the length of the base is 4 cm. What is the angle between the ABV and BCV planes? ABCD is the base, V is the vertex.
Square pyramid
Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side base has an angle of 60 degrees.
Cone
The rotating cone volume is 9.42 cm³, with a height of 10 cm. What angle is between the side of the cone and its base?
In a regular 5
In a regular triangular prism ABCV, the deviation of the side wall and the base plane is α = 45°. Determine the deviation of the side edge and the base plane.
Aircraft climbing
The average climb angle of the aircraft is 11° 20', and its average speed is 400 km/h. How long does it take to climb to a height of 3000m?
Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base is 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³.
Pyramid
The pyramid has a base a = 2cm and height in v = 7 cm. a) calculate the angle between plane ABV and the base plane b) Calculate the angle between the edges on the opposite side.
Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1°
Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each of the two forces.
Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
Angle of cone
The cone has a base diameter of 1.5 m. The angle at the central apex of the axial section is 86°. Calculate the volume of the cone.
The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
Motion on circle
The bend has a radius of r = 100 m and is inclined at an angle of 20° to the horizontal plane (= tilt angle). What is the safe (the "best") speed to go through this curve? Sketch the picture regarding NIVS, mark the forces, and calculate.
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].
Earth parallel
Earth's radius is 6377 km long. Calculate the length parallel to latitude 75°.
Boat
A force of 240 kg (2400 N) is required to pull a boat up a ramp inclined at 10° with horizontal. How much does the boat weigh?
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.
An azimuth
The patrol had started at a designated marching angle (an azimuth) of 13°. After 9 km, the azimuth's angle changed to 62°. The patrol went 10 km in this direction. Find the distance from where the patrol started.

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