Solid geometry, stereometry - page 106 of 121
Number of problems found: 2403
- Earth's surface
The greater part of the Earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land? - Diameter 7648
The mug has the shape of a cylinder with a height of 60.7 mm. There is two dl of water in it. If we dip a ball with a diameter of 40 cm into the water, the water will not overflow. What is the minimum diameter of the cup? - Cone and the ratio
The rotational cone has a height of 43 cm, and the ratio of the base surface to the lateral surface is 5: 7. Calculate the surface of the base and the lateral surface. - Cube-shaped 2751
What weight will a cube-shaped concrete base with an edge length of 10 m have if one concrete cube weighs 2200 kilograms? - Ratio-cuboid
The lengths of the edges of the cuboid are in the ratio 2:3:6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - Assume
Two naughty boys broke the glass on the front door. The glass was 105 cm, 150 cm, and 6 mm thick. They decided to buy the glass from their savings and, since they assumed that it would not weigh more than 12 kg, they would bring it and ask the caretaker t - Quadrilateral 22003
The shelter has the shape of a regular quadrilateral pyramid without a front wall. The length of the base edge is 3 meters, and the shelter's height is 3.5 meters. How much canvas must be bought to sew it if we have to increase consumption by 20% for fold
- Ball screen
The diameter of the ball screen is 30 cm. If we add 5% of the material to be sewn, how many m² of fabric do we need to make? - Allowances 82413
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 - Percentage 81914
The carpenter worked on a rotary cylinder with a base radius of 2.5 dm and a height of 2 dm. He reduced the radius by 1 cm by uniform grinding, and the height of the cylinder was preserved. Calculate the percentage by which the volume of the cylinder has - Circumference 4255
The rectangle has a circumference of 24 cm so that its area is maximum and its length is larger than its width. Find the dimensions of a rectangle. - Circumference 27161
Sketch the cone mesh and add the side length, the arc length of the circle, and the circle length to it, if you know: the side length of the cone: s = 51.9 cm cone base circumference = O = 151 mm. - Tower
The top of the tower is a regular hexagonal pyramid with a base edge 6.1 meters long and a height 11.7 meters. How many m² of the sheet is required to cover the top of the tower? We must add 9% of metal for waste. - Circumference 30781
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? - Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3:5. Calculate the surface and volume of the cone if its height v = 4 cm.
- CuZn
Brass is an alloy of copper and zinc. The 10-centimeter brass cube weighs 8.6 kg. Copper density is 8930 kg/m3, the zinc density is 7130 kg/m³. Calculate how many kilograms of copper and zinc a cube contains. - Determine 67764
The barrel filled with asphalt has a diameter of 60 cm and a height of 100 cm. The weight of the asphalt in it is 390 kg. Determine the density of the asphalt. - 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? - Quadrilateral 23891
A cylinder with the maximum possible base was ground from a wooden regular quadrilateral prism (edge 2.8 cm, height 7.5 cm). What percentage of the material was wasted as waste? What percentage would it be if the height of the prism were twice as large? - Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has an area of 10 cm². Find the area of the or
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