Geometry - math word problems - page 160 of 162

Number of problems found: 3232

Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c have dimensions in the ratio of 10:8:9. If you know that the diagonal wall AC is 75 cm, and the angle between AC and space diagonal AG is 30 degrees.
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.
Cuboid
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees).
Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle
Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0cm is submerged in the cone. Find the volume of water below the sphere.
Ballistic curve
The soldier fired the ballistic grenade at a 45° angle. The first half ascended, and the second fell. How far and height did it reach if his average speed was 1200 km/h, and what 12 seconds were taken from the shot to impact?
Calculate cone
The rotating cone has a base radius r = 226 mm, and the deviation of the side from the base plane is 56°. Calculate the height of the cone.
Quadrilateral prism
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base.
Cube - angles
Calculate the angle alpha (α) between the wall diagonal and cube base. Calculate the angle beta (β) between the cube body diagonal and the cube base.
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
Tropical, mild and arctic
How many percent of the Earth's surface lies in the tropical, mild, and arctic ranges? The border between the ranges is the parallel 23°27' and 66°33'.
Triangle KLB
It is given an equilateral triangle ABC. From point L, the midpoint of the side BC of the triangle, it is drawn perpendicular to the side AB. The intersection of the perpendicular and the side AB is point K. How many percent of the area of the triangle AB
Cuboid
Find the dimensions of cuboids a, b, and c; if diagonal d=9 dm has an angle with edge α=55° and has an angle with edge b β=58°
Determine the surface area
Find the surface area of a cone of height 30 cm whose side makes an angle of 60° with the base plane.
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'.
Raindrops
The car runs on a horizontal track at a constant speed of 20 m²-1. It is raining. Raindrops fall in a vertical direction at a speed of 6 m/s. a) How fast is the speed of the drops relative to the car windows? b) What is the angle of the raindro
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.
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.
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.

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