Examples for secondary school students - page 182 of 237
Number of problems found: 4731
- Axial cut
The cone surface is 388.84 cm2, and the axial cut is an equilateral triangle. Find the cone volume. - Pyramid 4sides
Calculate the volume and the surface of a regular quadrilateral pyramid when the edge of the base is 4 cm long, and the pyramid's height is 7 cm. - Support colum
Calculate the support column's volume and surface. It is shaped as a vertical quadrilateral prism whose base is a rhombus with diagonals u1 = 102 cm and u2 = 64 cm. The column height is 1. 5 m. - Traffic cones
Forty identical traffic cones with a base diameter d = 3 dm and height v = 6 dm will be painted orange outside (without the base). If we need 50 cm³ of paint to cover 1 m² and 1 liter of paint costs 80 SKK, how many SKK crowns will we pay? - Roof 8
How many liters of air is under the tower's roof, 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. - Apples
A 2 kg of apples cost a certain sum of money. This sum equals the number of kilograms for which we pay 72 CZK. How much is 1 kg of apples? - Vase capacity
The cylindrical vase is 28 cm high. Its inner diameter d = 1.1 dm. How many liters of water will fit in it if the bottom thickness is 1.5 cm? - Water height
The cylindrical container with a diameter of 1.8 m contains 2000 l of water. What height does the water reach? - Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm. - Cube diagonals
If you know the length of the body diagonal u = 216 cm, determine the cube's volume and surface area. - Price reduction
The price of the device is reduced by one-fifth every year. How long before the price of the device drops to one-tenth of the price? Specify years and months with precision. - Algebrogram
Solve cryptarithmetic (alphametics) for a sum of three numbers: BEK KEMR SOMR ________ HERCI - Pyramid
The pyramid has a base rectangle with a = 6 cm and b = 8 cm. The side edges are the same, and their length is 12.5 cm. Calculate the surface of the pyramid. - Polygon angle
A regular 15-angle is given. A triangle is formed if we connect points 3 and 7, 13 and 10. The vertices are 3 and 13, and the lines' intersections are 3.7 and 13.10. We are to determine the angle size formed by sides 3.7 and 13.10. These numbers indicate - Cuboid and ratio
A cuboid has dimensions in a ratio of 1:2:6, and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid. - Cone
The rotating cone volume is 9.42 cm3, with a height of 10 cm. What angle is between the side of the cone and its base? - Folded square
ABCD is a square. The square is folded on the midpoint of AB, and A is folded onto the fold, creating a shaded region. The perimeter of the shaded figure is 75. Find the area of square ABCD - Money distribution
Pavol, Edita and Juraj have a total of 1243 euros. Pavol has 200 euros more than Edita, Juraj has 457 euros less than Edita. Determine how much each has. - Hexagonal pyramid
A regular hexagonal pyramid has dimensions: the length edge of the base a = 1.8 dm, and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid. - Cone surface Calculate the surface and volume of the rotating cone, whose base circumference is 125.6 cm and the side is 25 cm long.
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