Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.

Stereometry deals with 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: 963

Cube containers
Replace the two cube-shaped containers with 0.8 dm and 0.6 dm edges with a single cube-shaped one so that it has the same volume as the two original ones together. What is the length of the edge of this cube?
Volume per time
How long does fill take for a pump with a volume flow of 200 l per minute fill a cube-shaped tank up to 75% of its height if the length of the cube edge is 4 m?
The wooden
The wooden block measures 12 cm, 24 cm, and 30 cm. Peter wants to cut it into several identical cubes. At least how many cubes can he get?
Into box
How many cubes with an edge of 2.5 cm fit into a box measuring 11.6 cm; 8.9 cm and 13.75 cm?
Cargo space
The cargo space of the truck has the dimensions a = 4.2 m, b = 1.9 m, c = 8.1 dm. Calculate its volume.
Jansen
Jansen had 1.3 litres of fruit juice. He drank 0.5 litres during lunch. How many litres of fruit juice does he have left?
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 volume of the segment. What is the distance of the cutting plane from the center of the sphere?
Aquarium
How many liters of water can fit in an aquarium measuring 30, 15 and 20 cm?
Ice floe
What is the volume of an ice floe weighing 326 kg? The density of ice is only 920 kg/m3.
The body
The body has dimensions of 2m 2dm and 10 cm. It weighs 28 kg. What is its density?
Brick wall
What is the weight of a solid brick wall that is 30 cm wide, 4 m long and 2 m high? The density of the brick is 1500 kg per cubic meter.
Thousand balls
We have to create a thousand balls from a sphere with a diameter of 1 m. What will be their radius?
Wooden block
A cuboid-shaped wooden block has 6 cm length, 4 cm breadth, and 1 cm height. Two faces measuring 4 cm x 1 cm are colored in black. Two faces measuring 6 cm x 1 cm are colored in red. Two faces measuring 6 cm x 4 cm are colored in green. The block is divid
Gas sphere
The gas tank has the shape of a sphere with a diameter of 14 m. How many m³ of gas will fit in it?
Clay balls
How many clay balls with a radius of 1 cm can be made from a ball of clay with a radius of 8 cm?
Two walls
Calculate the surface area of a cube in m² if you know that the area of its two walls is 72 dm².
Equilateral cone
We pour so much water into a container that has 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?
Candles
Before Christmas, Eva bought two cylindrical candles - red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 p. M. , lit a green candle at 7:00 p. M. , and left them both on fire until they burned. At 9:30 p. M. , bo
The cylinder
The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder.
Twice of radius
How many times does the surface of a sphere decrease if we reduce its radius twice?

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