# 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.- 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? - Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =? - Chocolate roll

The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this. - Pyramid four sides

In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters. - Wall diagonal

Calculate the length of wall diagonal of the cube whose surface is 384 cm square. - The cylinder base

The cylinder with a base of 8 dm^{2}has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level? - Cube walls

Find the volume and surface area of the cube if the area of one wall is 40cm2. - Triangular prism

The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm^{2}and the body height is 10 cm. Calculate the body volume. - Cone

Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long. - Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Trapezoidal prism

Calculate the surface of the quadrilateral prism ABCDA'B'C'D 'with the trapezoidal base ABCD. The height of the prism is 12 cm; ABCD trapezoidal data: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diagonal length is 7 cm. L - Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm. - Solid cuboid

A solid cuboid has a volume of 40 cm^{3}. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Surface area of the top

A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder. - Triangular prism

Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm - Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Regular quadrangular pyramid

The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes? - Ratio of edges

The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.

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