Solid geometry, stereometry - page 62 of 123

Number of problems found: 2441

Cuboid cone volume
We used the same amount of paint to paint a cuboid with dimensions of 10 cm, 15 cm, and 3 cm to paint the shell of a cone whose radius is 8 cm. How tall is this cone? Calculate its volume in liters.
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.
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
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)
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.

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