Solid geometry, stereometry - page 96 of 121
Number of problems found: 2404
- An architect 2
An architect is designing a house. He wants the bedroom to be 8 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume of the bedroom. Sol - Cone and cube
About what percentage has cone with base radius r larger volume than a same high cube with square base with edge length r? - Cone-shaped 8170
How many cone-shaped cones will we have to take to fill 20 l of creams (to the brim) if the cone has an inner base diameter of 6 cm and a height of 8 cm. Make a drawing, and write the answer. - Barrel of oil
The barrel of oil weighs 283 kg. When it molded 26% oil, it weighed 216 kg. What is the mass of the empty barrel? - Hexagon rotation
A regular hexagon of side 6 cm is rotated at 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - Lathe
From the cube of edge, 41 cm was a lathed maximum cylinder. What percentage of the cube is left as waste after being lathed? - The pool - optimization
A block-shaped pool with a volume of 200 m³ 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 - 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 - Five-sevenths of a volume
Forty-two liters of water fill the barrel to two-thirds of its volume. If it is filled to five-sevenths of a volume, how many liters of water do we need to add? - Cone in cube
The cube is an inscribed cone. Determine the ratio of the volume of the cone and cube. Please write the ratio as a decimal number and as a percentage. - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Volume of three cuboids
Calculate the total volume of all cuboids for which the edges' sizes are in a ratio of 1:2:3, and one of the edges has a size of 6 cm. - Hole
We will drill the cylinder shape hole in the cube's center with an edge 16 cm. The volume of the hole must be 10% of the cube. What should drill diameter be chosen? - Precisely 64114
We painted a wooden cube with an edge 4 cm long with green paint over the entire surface. Then we cut it into small cubes with an edge length of 1 cm. The number of cubes that have precisely two faces colored green is: - Cuboid - ratio
Find the volume of a block whose dimensions are in the ratio 2:3:4 and the surface is 117 dm². - Cone
The circular cone has height h = 15 dm and base radius r = 2 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane if solids have the same volume. - Water container
The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container? - If we want
A children’s pool has the shape of a cylinder with a base diameter of 4 m and a depth of 50 cm (sketch, calculation, answer). a) Calculate the volume of water in liters that can be in the pool if it is filled to the brim. b) If we fill the pool only 75%, - Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent the waste was. - Foundations 25831
How many kilograms of cement are used to concrete the foundations under the machine if the concrete slab has the shape of a cuboid 4.6 m long, 2.7 m wide, and 45 cm high if 250 kg of cement is used per 1 m³?
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