Solid geometry, stereometry - page 61 of 123
Number of problems found: 2442
- The circumference 3
The circumference of a cylindrical water tank is 62.8 m. When it is 4/5 full of water, it holds 125.6 hectoliters. Find the depth of the tank. - The height of prism
The base of a vertical prism is a right triangle with legs 30 cm and 40 cm long. The prism has the same volume as a cube with an edge length of 3 dm. Find the height of the prism in centimetres. - Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's area. Calculate the area of the upper base. - Pool water height
The pool has dimensions of 4.8 m and 65 dm. To what height is water filled in a pool if there is 1,029.6 hl of water in it? - Rotating cone
If the side of the rotating cone is 150 mm long and the circumference of the base is 43.96 cm, find its surface and volume. - Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1. - 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 = 4.6 dm and the height v = 230 mm. - 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. - Prism
Calculate the height of a prism with a total surface area of 448.88 dm² and a square base with a side of 6.2 dm. What is its volume in hectolitres? - The cylinder base
A cylinder with a base area of 8 dm² has a volume of 120 litres. From the cylinder, which was full of water, 40 litres were removed. At what height from the bottom (to the nearest dm) is the water level? - 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. - Insulation
A special rubber pipe insulator is used to insulate the supply pipes of solar collectors. The product with the description DNa20, thickness 25 mm, 2 m corresponds to insulation for pipes with a diameter of 20 mm and a rubber layer thickness of 25 mm, sold - 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? - Honeycomb capacity
The honeycomb comprises cells with the shape of a regular 6-sided prism with a base edge length of 3 mm and a corresponding height of 2.6 mm. The height of the prism is 12 mm. How many liters of honey are there in the entire comb if the plastic comprises - Paint needed
The janitor is to paint the computer room walls, which are 7 m long, 5 m wide and 3 m high. The classroom has four square windows with a length of 1 m and a door 1 m wide and 2 m high. At least how many kilograms of paint should he buy if 1 kg of paint pa - 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. - From a full
From a full cylindrical glass with a diameter of 8 cm, 1 decilitre of water was poured out. By how many centimetres did the water level in the glass drop? - Quadrilateral prism
Calculate the surface and volume of a quadrilateral prism if given: the area of the base is 40 cm², the bottom of the base is k = 8 cm, and the height of the prism is 1.3 dm (the bottom is a rectangle)
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