Solid geometry, stereometry - page 62 of 121
Number of problems found: 2410
- Two hemispheres
In a wooden hemisphere with a radius r = 1, the carpenter created a hemispherical depression with a radius r/2. The bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)? - Cone measurements
Calculate the volume and surface of the rotating cone with the base radius r = 4.6dm and the height v = 230mm. - Cone volume
The area of the rotating cone shell is 240 cm2, and the area of its base is 160 cm². Calculate the volume of this cone. - Cone container The Rotary cone-shaped container has a volume of 1000 cubic cm and a height of 12 cm. Calculate how much metal we need to make this package.
- Stadium
A domed stadium is shaped like a spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the dome's height at its center to the nearest tenth of a meter. - Quadrilateral prism + water
We poured water up to a height of 34 cm into a container of a regular quadrilateral prism with a base edge a = 10.6 cm and a wall diagonal of 3.9 dm. We then inserted a 6 cm long cylinder with a diameter of 10 cm. How many liters of water overflowed? - Pine wood
We cut a carved beam from a pine trunk 6 m long and 35 cm in diameter. The beam's cross-section is in the shape of a square, which has the greatest area. Calculate the length of the sides of a square. Calculate the volume of lumber in cubic meters. - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Cheops pyramid
The Pyramid of Cheops is a pyramid with a square base with a side of 233 m and a height of 146.6 m. It is made from limestone with a density of 2.7 g/cm³. Calculate the amount of stone in tons. How many trains with 30 twenty-ton wagons carry the stone? - Top-open tank
The top-open tank resembles a truncated rotating cone, standing on a smaller base. Its volume is 465 m3, and the bases' radii are 4 m and 3 m. Find the tank's depth. - Water height
The water tank has the shape of a block. The bottom of the tank is square, with a side length of 3 m. There are 22,500 liters of water in the tank. To what height in meters does the water in the tank reach the specified amount? - Cuboid diagonals
The cuboid has dimensions of 15, 20, and 40 cm. Calculate its volume and surface, the length of the body diagonal, and the lengths of all three wall diagonals. - Cube dimension calculation
The cube has an area of 486 dm². Calculate the length of its side, its volume, the length of the body, and wall diagonals. - Volume of the cone
Calculate the cone's volume if its base area is 78.5 cm² and the shell area is 219.8 cm². - Sphere parts, segment
A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. What are the volume and surface of the segment? - Reservoir height calculation
The block-shaped reservoir has 147 hl of water and is 3.5 m long and 2.8 m wide. Calculate its height. - Pyramid casting weight
The regular quadrilateral pyramid-shaped casting, with a base edge 60 cm in length and 5 cm in height, is made of a material density of 7.8 g / cm 3. Calculate its weight. - Tetrahedral pyramid
A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area). - Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Pyramid measurements
The regular hexagonal pyramid has a base edge of 20 cm and a side edge of 40 cm. Calculate the height and surface of the pyramid
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