Solid geometry, stereometry - page 33 of 123

Number of problems found: 2441

Aquarium volume
The aquarium is shaped like a cube and is partially filled with water. For Peter, a cube with an edge of 8 cm fell into it and completely sank. The water level in the aquarium rose by 1 cm. What is the volume of the whole aquarium?
Tetrahedral prism
The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge if you know that the prism volume is 2187 cm³.
Prism X
The prism with the edges of the lengths x cm, 2x cm, and 3x cm has a volume 29478 cm³. What is the area of the surface of the prism?
Three-quarters of volume
A cylindrical container is three-quarters full with six liters of water. We dip a cube-shaped body into the container, which sinks to the bottom. The length of the edge of the cube is 13 cm. Decide what happens to the sink after the cube is dipped.
Eight
Eight small Christmas balls with a radius of 1 cm have the same volume as one large Christmas ball. What has a bigger surface: eight small balls or one big ball?
Cylinder height surface
The volume of the cylinder is 193 cm³, and the radius of its base is 6.4 cm. Calculate the height and surface of the cylinder to 1 decimal place.
Block cube edge
The block and the cube have the same volumes of 512 cm³, and the block has edge lengths of b = 6.4 cm and c = 10 cm. Can a cube and a block have the same edge length?
Candle edge enlargement
The candle is shaped like a block measuring 3 cm, 4 cm, and 5 cm. If we gradually enlarge one, two, and all three edges twice, how many times is more wax used to make a candle?
Funnel radius calculation
The conical funnel has a volume of 0.5 liters and a height of 7 cm. Calculate the radius of its upper edge.
Cube Edge Size Volume
The road is paved with 2500cm cubic cubes. Calculate the edge size to the nearest millimeter.
Cube volume edge
1. Calculate the volume of a cube whose edge is 3.6 dm long. 2. Calculate the edge's size if you know its surface S = 2166 mm².
Pyramid height calculation
The base of the prism is a square with a side of 10 cm. Its height is 20 cm. Calculate the height of a pyramid with a square base of 10 cm, which has four times the prism's volume.
Cylinder diameter calculation
Calculate the diameter of a cylinder 7.5 dm high with a volume of 0.6 hl. Express the result to the nearest centimeter.
Cube dimensions
The red cube has an edge 0.2 dm smaller than the blue cube. The surface of the blue cube is 294 cm². What are the dimensions of the cubes?
The surface
The surface of a truncated rotating cone with side s = 13 cm is S = 510π cm². Find the radii of the bases when their difference in lengths is 10 cm.
Cube surfce2volume
Calculate the volume of the cube if its surface is 150 cm².
Spherical segment
Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, and the upper base is 60 cm.
The cube
The cube has a surface area of 216 dm². Calculate: a) the area of one wall, b) edge length, c) cube volume.
Diameter = height
The cylinder's surface, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
Truncated cone and sphere
A sphere is inscribed in a truncated cone with base diameters D1=10 cm and D2=20 cm, touching both bases and the surface. What is its diameter?

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