# Angle + surface area - math problems

#### Number of problems found: 49

- The roof

The roof of the tower 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 an angle of 57°. Calculate how much roofing we need to cover the entire roof, if we count on 15% waste - Base diagonal

In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Side edges

The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - A spherical segment

The aspherical section, whose axial section has an angle of j = 120° in the center of the sphere, is part of a sphere with a radius r = 10 cm. Calculate the cut surface. - Quadrilateral prism

The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism. - 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 surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele - Quadrilateral pyramid

In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place. - 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. - Triangular prism

Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm. - Tropics and polar zones

What percentage of the Earth's surface lies in the tropical, temperate, and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'. - Quadrilateral prism

Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - 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 is needed to cover the top of the tower if 15% extra sheet metal is needed for joint - Hexagonal pyramid

Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. - Quadrilateral pyramid

In a regular quadrilateral pyramid, the side edge is e = 7 dm, and the diagonal of the base is 50 cm. Calculate the pyramid shell area. - Two bodies

The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco - Cone side

Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side. - Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Hexagon

Calculate the regular hexagonal prism's surface whose base edge a = 12cm and side edge b = 3 dm. - Prism diagonal

The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism? - Octagonal tank

The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.

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Angle Problems. Examples for the calculation of the surface area of the solid object .