# Body volume + right triangle - math problems

- Base of prism

The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm^{2}. - Axial section

Axial section of the cone is an equilateral triangle with area 208 dm^{2}. Calculate the volume of the cone. - Cuboid

Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm^{3}. Calculate the length of the other edges. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm^{2}. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - Cone

Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°. - Circular pool

The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - Tetrahedral pyramid

Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone. - 4side pyramid

Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - Road embankment

Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters? - Tetrahedral pyramid

Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm^{2}and deviation angle of the side edges from the plane of the base is 60 degrees. - Triangular pyramid

Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm. - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees. - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm. - 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. - Two balls

Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - Hexagonal prism

The base of the prism 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. Calculate the volume and surface of the prism! - Triangular prism

Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.

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