Solid geometry, stereometry - page 119 of 121
Number of problems found: 2402
- Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and whose body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Base RR odd
The base of the prism is an isosceles trapezoid ABCD with bases AB = 12 cm, and CD = 9 cm. The angle at vertex B is 48° 10'. Determine the volume and area of the prism if its height is 35 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? - Pyramid
The pyramid has a base a = 3cm and height in v = 15 cm. a) calculate the angle between plane ABV and the base plane b) Calculate the angle between the edges on the opposite side. - 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. - Cross-section of a roof
The owner must cover the carport with a hipped roof with a rectangular cross-section of 8 m x 5 m. All roof surfaces have the same slope of 30°. Determine the price and weight of the roof if 1 m² cost €270 and weighs 43 kg. - House volume
V = 35 m α = 55° β = 15° ----------------- X =? Calculate: V- barrack volume =? S- barrack area =?
- An Elizabethan collar
An Elizabethan collar is used to prevent an animal from irritating a wound. The angle between the opening (diameter 6 inches) with a 16-inch diameter and the side of the collar is 53 degrees. Find the surface area of the collar shown. - 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. - 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? - 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. - 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. - 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. - 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. - Box
Calculate the angle between box base 9 x 14 and body diagonal length 18.
- 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. - 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. - 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. - 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.
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