Volume + diagonal - practice problems
Number of problems found: 109
- Calculate 415
Calculate the cuboid's dimensions if the sum of its edges is 19cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - Quadrilateral 83307
The diagonal of section DBFH of the regular quadrilateral prism ABCDEFGH inscribes a circle with a diameter of 8 cm. What is the volume of the prism? - Quadrilateral 83254
What is the volume of a regular quadrilateral pyramid if its base edge a = √18 cm and side edge b = 5 cm? - Tetrahedron 83144
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise?
- Calculate 83044
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and body diagonals. - Calculate 82567
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - ABCDEFGH 82499
In the cube ABCDEFGH, the area of triangle ABK is √20 cm². How much cm² is the volume of ABGH in a cube if you know that K is the midpoint of edge CG? - Calculate 82458
Calculate the volume of a cube with a wall diagonal of u = 20 cm. - Quadrilateral 82146
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base.
- Quadrilateral 82066
Calculate the volume of a regular quadrilateral pyramid with a square base of side a = 3 cm and side length b = 7 cm. - Inscribed 81949
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - Dimensions 81608
Find out if a circle with a volume of 38.5 cm² fits into a rectangle with dimensions of 110 mm and 65 mm. - One-third 77724
The cuboid has a body diagonal u=25 cm, and side b is one-third longer than side a. What is the volume of the cuboid? - Calculate 70634
The axial section of the cylinder is a rectangle with a diagonal of u = 20 cm. The height of the cylinder is twice the diameter of the base. Calculate the cylinder volume in liters.
- Measuring 65374
Calculate the length of the body diagonal of a block measuring 6 cm, 7 cm, and 10 cm, and round the result to two decimal places. - Quadrangular 64724
The decorative object has a quadrangular pyramid shape, the base edge is 0.7 dm, and the side edge is 1.4 dm long. Calculate the height of the object. - Calculate 64654
Calculate the length of the wall and body diagonal in a cube with an edge of 60 cm. - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - A prism
A prism with an altitude of 15cm has a base in the form of a regular octagon inscribed in a square of 10cmx10cm. Find the volume of the prism.
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