Angle + surface area - practice problems - page 2 of 4
Number of problems found: 71
- Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism? - 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. - Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m. The pyramid height is 1.6 m. How many square meters of sheet metal are needed to cover the top of the tower if 15% extra sheet metal is needed for join - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c has dimensions in the ratio of 7:8:10. If you know that the diagonal wall AC is 56 cm, and the angle between AC and space diagonal AG is 25 degrees.
- 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'. - Deviation 70434
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 tank
The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, and the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness. - Circular 4690
The cone shell with a base radius of 20 cm and a height of 50 cm unfolds into a circular cutout. How big is the center angle of this cutout? - Hexagonal prism
The prism's base is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism.
- Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - Determine 82032
Determine the volume and surface area of a cone whose slope of length 8 cm makes an angle of 75 degrees with the plane of the base. - Hexagonal 3468
The box of a regular hexagonal prism is 4 cm high, and the lid has sides 20 cm long. How much cardboard is needed to make it? (No part is double) - Big Earth
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km. - Calculate 6566
Calculate the surface area and volume of a regular hexagonal pyramid whose base edge is 10 cm long and the side edge is 26 cm long.
- Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid. - Hexagon
Calculate the regular hexagonal prism's surface whose base edge a = 12cm and side edge b = 3 dm. - Tower
How many m² of the copper plate should be replaced on the roof of the conical tower shape with a diameter 23 m, and the angle at the axial section's vertex is 119°? - Octahedron
All walls of the regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron. - Calculate 82567
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.
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