Solid geometry, stereometry - page 103 of 121
Number of problems found: 2409
- Roof cover
Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m² of sheet metal is needed to cover this roof; if 5.5% of the sheet, we must add for joints and waste. - The glass
1 m³ of glass weighs 2600 kg. Calculate the weight of the glass glazing panel with dimensions of 2.5 m and 3.8 m if the thickness of the glass is 0.8 cm. - Stone
When Peter threw a stone in a water box, he discovered that the water level had risen by 9 cm. The box has a cuboid shape, the bottom has dimensions of 24 cm and 14 cm, height is 48 cm. What volume has a stone? - Block cover fabric
The teacher decided to sew covers for the eight-seat blocks in the school library. All cubes are cube-shaped with an edge 40 cm long. How many m² of fabric will the teacher need in total if the blocks are not lined from the bottom, and 5% must be added fo - Pyramid cutting calculation
The regular quadrilateral pyramid has a height of 40 cm and a base side of 21 cm. Cut the needle at half the height. How much will both parts have? - Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal? - The body
The body on the figure consists of cubes with an edge length of 7 cm. What surface has this body? - Carnival hat paper
How many square decimeters of decorative paper are needed to make cone-shaped carnival hats for 46 first-graders if the first-graders head circumference is 49 cm and the cap height is 33 cm? Is it necessary to add 3% paper to the folds? - TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have - Volume of sphere
How many times does the volume of a sphere increase if its radius increases two times? - Cube Edge Volume Change
How does the volume of a cube change if we double the length of its edge? - Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums? - Sun density
The volume of the Sun is 1.4x10 per 18 km cubic, and the weight is 2x10 per 30 kg. What is the average density? (in kg/m cubic) - Copper wire
What is the weight in kg of copper wire 200 m long with a diameter of 0.6 cm if the density of copper is 8.8 kg/dm³? - Tent fabric calculation
The children's tent with a beech wood floor has the shape of a regular four-sided pyramid with a base edge of 1.25 m and a height of 80 cm. How much m² of fabric do we need to finish the tent if we add 12% material to the folds? - Store - silo
A cylindrical silo (d = 4 m, h = 8 m) is about 70% full. How many m³ of silage are stored in it? Round the result to a whole number. - Seat
How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if we add 10% of the material to the folds? - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an - Prism + rhomboid
The prism-shaped vessel with a rhomboid base has one base diagonal of 10 cm and the edge of the base 14 cm. The edge of the base and the prism height are in a ratio of 2:5. How many liters of water is in the container when it is filled to four-fifths of t - Shot casting
How many shots with a diameter of 2 mm can a gunsmith cast from 1 kg of lead? The density of lead is 11.4 g / cm3
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