Pythagorean theorem - practice for 14 year olds - page 28 of 44
Number of problems found: 868
- What percentage
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km. - Perimeter 83259
The perimeter of the four-sided needle is 48 m, and its height is 2.5 m; how much will the sheet metal for this pyramid cost? If 1m² costs €1.5, a 12% loss due to joints and folds is included in the area. - Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2:3. Calculate its volume if you know its area is 314 cm square. - Float boya
A 0.5-meter spherical float is a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and saltwater weighs 1027 kg/m³.
- Pyramidal 44061
A pyramidal candle with a square base has a side edge of s = 12 cm and a base edge of 4 cm. How much wax will we need to make it, and how long is the wick if it is 5% bigger than its height? - Four-sided 15613
The turret has the shape of a regular four-sided pyramid with a base edge 0.8 m long. The height of the turret is 1.2 m. How many square meters are needed to cover it, counting the extra 10% sheet metal waste? - Four-sided 5957
How much m² of the galvanized sheet is used to cover the roof of the tower, which has the shape of a four-sided pyramid, whose base edge is 6 m long? The height of the tower is 9m. When covering, is 5% metal waste expected? - Coverage 71484
The tower's roof is a regular 4-sided pyramid with a height of 4m and an edge of the base of 6m. 25% of the roof covering was found to be damaged. How many square meters of coverage are needed to repair the roof? - Pyramid-shaped 8176
A block-shaped shed is covered with a quadrilateral pyramid-shaped roof with a base with sides of 6m and 3m and a height of 2.5m. How many m² (square meters) must be purchased if an extra 40% is calculated for roofing and waste?
- Pyramid-shaped 7820
The pyramid-shaped tent has a square base with a side size of 2.2m and a height of 1.8m. How many square meters of tent canvas are needed to make it if we count an extra five percent for the foundation? - Rotating 28501
Which bags shaped like the shell of a rotating cone can hold the most popcorn? The first bag has a height of 20 cm, and the length of its side is 24 cm. The second bag has a base radius of 10 cm and a height of 25 cm. - Felix
Calculate how much land Felix Baumgartner saw after jumping from 36 km above the ground. The radius of the Earth is R = 6378 km. - A Pile of salt
A Pile of salt has been stored in the shape of a cone. Mr. Terwilliker knows that the pile is 20 feet tall and 102 feet in circumference at the base. What area of the conical tarpaulin (a large sheet of material) is needed to cover the pile? - Quadrilateral 29201
How much sheet is needed for a roof with the shape of a regular quadrilateral pyramid if its edge is 2.8 m long and the height of the roof is 0.8 m?Calculate 10% for the overlap (extra).
- Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Find how many m³ of soil were excavated when digging the pit. - Cube from sphere
What largest surface area (in cm²) can have a cube that we cut out of a sphere with a radius 26 cm? - Equilateral 83322
The glass weight has the shape of a regular four-sided pyramid with a base edge of 10 cm. The shell walls are equilateral triangles. What is the weight in grams of the paperweight if the density of the glass is 2500kg/m³? - Administrator 23801
The administrator of the castle is trying to estimate how many square meters of sheet metal will be needed for the new roof of the tower. The roof has the shape of a cone. The castle administrator knows that the tower's diameter is 4.6 meters and its heig - Cone A2V
The cone's surface in the plane is a circular arc with a central angle of 126° and area 415 cm². Calculate the volume of a cone.
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