Physical quantities - math word problems - page 290 of 292

Number of problems found: 5839

Quadrilateral prism
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the space diagonal makes an angle of 66° with the base.
Isosceles triangle
What are the angles of an isosceles triangle ABC if its base is long a=7 m and has an arm b=9 m?
Climb
The road sign that informs the climb is 10.3%—the car drives 10 km along this road. What is the height difference that the car went?
Periodic function
Simplify by using periodicity cos 1125°
Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees.
Earth's circumference
Calculate the length of the circle of latitude at 48°10′ on Earth.
Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal.
Pyramid - angles
In a regular pyramid in which the edge of the base is | AB | = 4 cm; height = 6 cm, calculate the angle of the lines AV and CV, V = vertex.
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.
4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
Cone
Calculate the volume and surface area of the cone with a diameter of the base d=16 cm and the side of the cone with the base has angle 37°12'.
Descent of road
A road sign shows a gradient of 10.9%. Calculate the angle of inclination of the slope.
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
Rotary cone
The volume of the rotation of the cone is 733 cm³. The angle between the side of the cone and the base angle is 75°. Calculate the lateral surface area of this cone.
Perpendicular direction
A speedboat moves relative to the water at a constant speed of 13 m/s. The speed of the water current in the river is 5 m/s a) At what angle concerning the water current must the boat sail to keep moving perpendicular to the banks of the river? b) At what
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.
Angle of two lines
There is a regular quadrilateral pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
Calculate a cone
The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone.
Diagonal
Determine the dimensions of a cuboid whose space diagonal is 60 dm and makes an angle of 35° with one edge and 77° with another edge.
Glass of juice
A cylindrical glass 13 cm tall with a base diameter of 9 cm is filled with juice to a level 3 cm below the rim. Determine the maximum angle to which the glass can be tilted without the juice spilling.

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