Solid geometry, stereometry - page 95 of 121
Number of problems found: 2404
- Surface of wall
Find by what percentage the cube's surface will decrease if we reduce the surface of each of its walls by 12%. - Decrease 80441
By what percent does a cube's volume decrease if its edge length is reduced by a quarter? - Integer cube
The length of the cube edge is an integer. Its volume is in cm3, a five-digit number divisible by 1331. What is the length of the edge of this cube? - Paper box
The hard rectangular paper has dimensions of 60 cm and 28 cm. We cut off the corners into equal squares, and the residue was bent to form an open box. How long must the largest volume of the box be beside the squares? - Dimensions 16913
The block's dimensions are in the ratio 16:12:8, and the sum of these dimensions is 240 decimetres. What are the dimensions of the block? - Dimensions 47111
The block's dimensions are 9:5:4. Determine its volume if you know that the sum of the longest and shortest edges is 65 cm. - Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm is an inscribed cylinder with maximum volume so that the cylinder axis is perpendicular to the cone's axis. Determine the dimensions of the cylinder. - Gold ring
A gold ring with a width of 1 cm is made by drilling a sphere with a radius of 1 cm through its center. A gold bracelet with a width of 1 cm is made by drilling a sphere with a radius of 4 cm through its center. Which piece of jewelry will be worth more i - Dimensions 81957
How many bricks are needed to build a wall that is 12 m long, 1.6 m high, and 47 cm wide if the dimensions of the brick are 30 x 15 x 7.5 cm and 5% of the wall volume is mortar? - Cylinder melted into cuboid
A circular cylinder has an area of cross-section of 56 cm², and the height is 10cm. The cylinder is melted into a cuboid with a base area of 16 cm². What is the height of the cuboid? - 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? - No smoke
Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. Regular cigarette contains 0.8 mg of nicotine. How much nicotine would a giant cigare - Cuboid - ratios
The sizes of the edges of the cuboid are in the ratio of 2:3:5. The smallest wall has an area of 54 cm². Calculate the surface area and volume of this cuboid. - Percentage - prism and cube
Prism with square base a=25cm, height h=45cm. cube: b=15cm a) what percentage of the volume of the prism is the volume of the cube? b) what height should the prism have to have the same volume as the cube? - Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in a ratio of 3:2. Volumes of a sphere and cuboid are in a ratio of 1:3. At what rate are the volumes of a cube, cuboid, and sphere? - Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center of the sphere? - 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-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?
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