Solid geometry, stereometry - page 96 of 123
Number of problems found: 2442
- Tanks
The fire tank is cuboid in shape, with a rectangular floor measuring 13.3 m × 14.7 m. The water depth is 1.9 m. Water was pumped from the tank into barrels with a capacity of 5 hl. How many barrels would have been used if the water level in the tank - The golf
The golf ball with a diameter of 43 mm is packed in a cube-shaped box. What percentage of the box volume is made up of a ball? - 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%. - 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? - Freezer box calculation
The freezer box has internal dimensions of 900 mm, 0.75 m, and 6 dm. 30% of the space is filled with frozen peppers packed in boxes measuring 150 mm, 100 mm, and 50 mm. How many boxes are in the box? - Cube volume decrease
By what percent does a cube's volume decrease if its edge length is reduced by a quarter? - Cuboid Dimensions Ratio Sum
The cuboid’s dimensions are in the ratio of 16:12:8, and the sum of these dimensions is 180 dm. What are the dimensions of the cuboid? - 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
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. - Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - 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? - 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? - Surface of cubes Peter molded a cuboid of 2 cm, 4 cm, and 9 cm of plasticine. Then, the plasticine was split into two parts in a ratio of 1:8. From each piece, a cube was made. In what ratio are the surfaces of these cubes?
- Wall brick count
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? - Well excavation transport
The company is to dig a well 25 m deep with a radius of 0.8 m. How many cars that can be loaded with 12 cubic m will be needed to transport the excavated soil if it is calculated that the soil will increase in volume by 10% when excavated? - 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? - Cube cylinder volume
There is a cylinder with the largest possible volume in the cube with an edge of 6 m. What percentage of the volume of a cube has the volume of a 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 - 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? - 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.
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