# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.- Common cylinder

I've quite common example of a rotary cylinder. Known: S1 = 1 m^{2}, r = 0.1 m Calculate : v =? V =? You can verify the results? - Megapascals

What is the area of crosssection of the piston, if the force of 300 kN produces a pressure of 5 MPa? - Hexagonal prism 2

The regular hexagonal prism has a surface of 140 cm^{2}and height of 5 cm. Calculate its volume. - Cuboid easy

The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid. - Shell of cylinder

Calculate the content of shell the 1.6 m height cylinder with a base radius of 0.4 m. - Roof 8

How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof. - Church roof 2

The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m^{2}of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste? - Painting a hut

It is necessary to paint the exterior walls of hut whose layout is a rectangle of 6.16 m x 8.78 m wall height is 2.85 meters. Cottage has five rectangular windows; three have dimensions of 1.15 m x 1.32 m and two 0,45 m x 0.96 m. How many m^{2}is necessary - Cube in sphere

The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere. - Stadium

A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter. - Axial cut

The cone surface is 388.84 cm^{2}, the axial cut is an equilateral triangle. Find the cone volume. - Body diagonal

Find the cube surface if its body diagonal has a size of 6 cm. - Regular quadrilateral pyramid

Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. - Wall height

Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm. - Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. - Cone

The rotating cone volume is 9.42 cm^{3}, with a height 10 cm. What angle is between the side of the cone and its base? - Cylinder horizontally

The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder? - Trench

The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil. - Pyramid

The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid. - Body diagonal

The cuboid has a volume of 32 cm^{3}. Its side surface area is double as one of the square bases. What is the length of the body diagonal?

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