Cube + triangle - practice problems - last page
Number of problems found: 59
- Prism
A right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 6 cm, has the same volume as a cube with an edge length of 1 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube - Perpendicular 79804
A perpendicular hexagonal prism was created by machining a cube with an edge length of 8 cm. The base of the prism is created from the square wall of the original cube by separating 4 identical right triangles with overhangs of lengths 3cm and 4cm. The he - Cube cut
The edge of the CC' guides the ABCDA'B'C'D'cube, a plane that divides the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine which ratio the edge AB divides by this plane. - The height of prism
A right triangle forms the base of the vertical prism with perpendiculars 30 cm and 40 cm long. This prism has the same volume as a cube with an edge length of 3 dm. Find its height in cm.
- Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has an area of 10 cm². Find the area of the or - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Surrounded 8283
The cube has an edge length of 5 cm. This cube surrounds a rotating cylinder. Find the surface area of the shell and the volume of the cylinder. - 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
- Quadrilateral 46431
Calculate the volume V and the surface S of a regular quadrilateral pyramid, the base edge and height of which are the same size as the edge of a cube with a volume V1 = 27m3 - 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. - 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? - An equilateral cone
Determine the radius and height (in centimeters) of an equilateral cone that has a volume of 1 liter. - 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.
- Cube and sphere
A cube with a surface area of 150 cm² is described sphere. What is a sphere surface? - 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. - 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? - Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
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