Cube - high school - practice problems - page 5 of 6
Number of problems found: 105
- Sphere area
A cube with an edge 1 m long is a circumscribed sphere (vertices of the cube lie on a sphere's surface). Find the surface area of the sphere. - Cube from sphere
What largest surface area (in cm²) can have a cube that we cut out of a sphere with a radius 26 cm? - Pyramid in cube
In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid. - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an
- Balls
Three metal balls with volumes V1=81 cm³ V2=96 cm³ and V3=28 cm³ melted into one ball. Determine its surface area. - Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume? - Identical 35961
Nine identical spheres are stacked in the cube to fill the volume of the cube as much as possible. What part of the volume will the cube fill?
- Rotary cone
A rotary cone whose height is equal to the circumference of the base has a volume 229 cm³. Calculate the radius of the base circle and the height of the cone. - The funnel
The funnel has the shape of an equilateral cone. Calculate the area wetted with water if you pour 3 liters of water into the funnel. - Block-shaped 7976
A block-shaped pool with a volume of 200m³ 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 - Sphere vs cube
How much % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere? - Funnel
The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water.
- Cube in sphere
The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius. - Cuboid edges in ratio
Cuboid edge lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm³. - Prism X
The prism with the edges of the lengths x cm, 2x cm, and 3x cm has a volume 29478 cm³. What is the area of the surface of the prism? - Dimensions 5996
How many cubes with an edge of 10 cm will fit into a block with dimensions of 2 dm, 3 dm, and 5 dm? - 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?
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