Goniometry and trigonometry - math word problems - page 29 of 32
Number of problems found: 624
- 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. - 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. - 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? - Deviation - slope angle
Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30° from the base plane. - 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'. - 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. - 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? - 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. - 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 - 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 - Earth parallel
Earth's radius is 6377 km long. Calculate the length parallel to latitude 75°. - 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 - 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 - 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. - 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? - 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. - Calculate cuboid
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH . - 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? - 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.
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