Solid geometry, stereometry - page 92 of 115
Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry involves the measurements of volumes of various solid figures (three-dimensional figures), including pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.
Number of problems found: 2289
- Angle of the sector
Find the angle of the sector of a circle radius of 20 units where the area is equal to the lateral area of a cone with a radius of 8 units. - Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid. - Block-shaped 7976
A block-shaped pool with a volume of 200m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Isosceles 3551
Jan and her father were going to the tent. They found that their old tent is torn. Their mother suggested that they sew a tent whose walls would be made up of six identical isosceles triangles. Their lower side is 2 m long, and the height to this side mea
- Dimensions 82810
The block has 10 cm, 20 cm, and 50 cm dimensions. We reduce the first edge of the cuboid by 20% and increase the second by 20%. How does the volume of the cuboid change? By how many percent? - Cylinder's 83288
Calculate the radius of the cylinder's base if its volume is equal to 12.56 cm². - Regular 4-sided pyramid
Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m. - An equilateral cone
Determine the radius and height (in centimeters) of an equilateral cone that has a volume of 1 liter. - The funnel
The funnel has the shape of an equilateral cone. Calculate the area wetted with water if you pour 3 liters of water into the funnel.
- Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³. - Rectangular cuboid
The rectangular cuboid has a surface area 5447 cm², and its dimensions are in the ratio 2:4:1. Find the volume of this rectangular cuboid. - Volume and body diagonal
Calculate how much the cuboid's volume and body diagonal decrease if we reduce each of its three edges, a, b, and c, by 18%. - Centimeters 82756
Let us have a cube whose edge length is expressed in centimeters and is a natural number. What is the smallest number of such identical cubes that can be made into a cuboid with dimensions of 24 cm, 32 cm, and 60 cm? How long will the edge of these cubes - Calculate 71324
Calculate the volume of a cube with a surface area of 1,795.74 cm2
- The pyramid
The pyramid with a square base is 50 m high, and the sidewall height is 80 m. Find the edge of the base of the pyramid. - Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - Calculate 82458
Calculate the volume of a cube with a wall diagonal of u = 20 cm. - Quadrilateral 82066
Calculate the volume of a regular quadrilateral pyramid with a square base of side a = 3 cm and side length b = 7 cm. - Calculate 75014
The surface of a cube is equal to 294 square meters. Calculate the edge and volume of the cube.
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