Solid geometry, stereometry - page 95 of 121
Number of problems found: 2418
- Inscribed sphere
How much % of the volume of the cube whose edge is 6 meters long is the volume of a sphere inscribed in that cube? - Granite sidewalk
On the sidewalk, 3 m wide and 8 m long, 2 m³ of mosaic stone (granite cubes) was used. The master of tiles had to pave the sidewalk 2.5 m wide and 65 m long. How much m³ of the stone does it consume? - Sugar cubes
The glass holds 600 ml of tea, which represents 80% of its volume. If twenty regular sugar cubes of 2 cm are poured into the tea, how many ml of tea are poured? - Water container
The container with water weighs 1.48 kg when we cast 75% of the water content of water weight 0.73 kg. How heavy is an empty container? - 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%. - Aquarium height calculation
The cuboid-shaped aquarium has the dimensions of the bottom: a = 0.7 m, b = 0.4 m. if it is filled to 90% of its volume and contains 75.6 liters of water? - 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? - Cone mass
The teacher brought to class two wooden models of cones, which were made of the same type of wood. The first model weighed 800g. The other had twice the base radius but half the height. Determine the mass of the second cone in grams. - Barrel 3
The barrel with water weighs 118 kg. When we get off 75% of water, it weighs 35 kg. How many kg has an empty barrel? - 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 - Cube volume decrease
By what percent does a cube's volume decrease if its edge length is reduced by a quarter? - 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. - 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? - 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? - 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?
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