Goniometry and trigonometry - math word problems - page 29 of 32
Number of problems found: 628
- Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - Quadrilateral prism
The body diagonal of a regular quadrilateral prism forms an angle of 60° with the base. The edge of the base is 20 cm long. Calculate the volume of the body. - Horizontal watertank
We have a horizontal tank shaped like a rainwater cylinder, 3.45 m long and 1.7 m wide. Calculate how many liters of water is in first centimeters. - Glass
How many glasses are needed to produce glass with a base of a regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm? - Refractive index
The light passes through the interface between air and glass with a refractive index of 1.5. Find: (a) the angle of refraction if light strikes the interface from the air at an angle of 40°. (b) the angle of refraction when light hits the glass interface - 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 - Earth parallel
Earth's radius is 6377 km long. Calculate the length parallel to latitude 75°. - Side deviation
Frustum has the base radii of the figures r1 and r2: r1> r2, r2 = s, and if the side deviation from the base plane is 60°. Express the surface and volume of the cone frustum using its side s. - Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the base plane is α = 60°. - Vertex angle - cone
The rotating cone has a height of 72 cm and an angle at the top of 72°. Determine the volume of a sphere with the same radius as the cone. - Calculate cuboid, diagonals
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - 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. - 9-sided pyramid
Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm - 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? - 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. - 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. - 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? - Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - 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.
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