# Right triangle + body volume - math problems

- 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? - A concrete pedestal

A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal. - Tetrahedral pyramid

A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area). - Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure. - Body diagonal

Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm - Space diagonal

The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube. - 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}. - Lateral surface area

The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm. - Pyramid height

Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm. - The diagram 2

The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm^{2}. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone - Triangular pyramid

What is the volume of a regular triangular pyramid with a side 3 cm long? - Triangular prism

Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm. - Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane. - Prism 4 sides

The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters - Quadrangular pyramid

The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area. - 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? - Axial cut of a rectangle

Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long. - Perpendicular prism

Calculate the volume of the perpendicular prism if its height is 60.8 cm and the base is a rectangular triangle with 40.4 cm and 43 cm legs. - Tetrahedral pyramid

Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m. - Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm^{3}.

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