# Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

- 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. - Cube into cylinder

If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge? - Pool tiles

The pool is 25m long, 10m wide and 160cm deep. How many m^{2}of tiles will be needed on the walls and the pool? How many pieces of tile are needed when 1 tile has a square shape with a 20cm side? How much does it cost when 1m2 of tiles costs 258 Kc? - Cube cut

The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '. - Spherical cap

Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm^{2}. Determine the radius r of the sphere from which the spherical cap was cut. - Metal rails

Dad needs to improve the edges of the wooden boxes - to be reinforced with metal rails. How many cms of rails will he need if the box has the shape of a prism with the length of the edges 70cm 70cm and 120cm? - Water flow 2

How many litres of water will flow in 7 minutes from a cylindrical pipe 1 cm in diameter, if the water flows at a speed of 30 km per hour - Surface area 6

Find the surface area of a prism whose bases are right triangles with sides of length 3, 4, and 5 inches and a height of 8 inches. Include a sketch - Pyramid height

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

Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g. - 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. - Paper box

Calculate whether 11 dm² of paper is sufficient for gluing a box without a lid with bottom dimensions of 2 dm and 15 cm and 12 cm high. Write result as: 0 = No, 1 = Yes - Distance of lines

Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm - A pipe

A radius of a cylindrical pipe is 2 ft. If the pipe is 17 ft long, what is its volume? - Height of the room

Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room? - A box

A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R? - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - Masquerade ball

Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm^{2}. - Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap. - Right triangular prism

We have cuboid with a base and dimensions of 12 cm and 5 cm and height of 4 cm. The tablecloth cut it into two identical triangular prisms with right triangular bases. The surface of the created prisms was painted with color. Calculate the surface area of.

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