Solid geometry, stereometry - page 72 of 123
Number of problems found: 2441
- Three faces of a cuboid
The diagonals of the three walls of a cuboid are 13, √281, and 20 units long, respectively. Thus, the cuboid's total surface area is. - 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? - Cube
The sum of all cube edges is 30 cm. Find the surface area of the cube. - Cube 53
A cuboid with a volume of 60 cm³ has a base with dimensions of 3 cm × 5 cm. Calculate the height of the cuboid in centimetres. - Quadrilateral pyramid
Construct a 3D model of a quadrilateral pyramid with a rectangle base and sides of isosceles triangles, with a volume of 80 cubic cm. I need to know the sides and the height. - Edge of prism
The regular quadrilateral prism has a surface of 250 dm². Its shell has an area of 200 dm². Calculate its leading edge. - Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach? - Calculate - prism
The base of the prism is a square with a side of 10 cm. Its height is 20 cm. Calculate the height of a pyramid with a square base of 10 cm, which has four times the prism's volume. - Rectangular base pyramid
The pyramid has a rectangular base of 2.8 m and 1.4 m and a height of 2.5 meters. Calculate an area of the shell of the pyramid. - Slant height
Find the cone's volume. The cone's slant height is 5 cm, and the radius of its base is 3 cm. - Diameter
What is the inside diameter of the cylinder container if half a liter of water reaches a height of 15 cm? - Cuboid and eq2
Calculate the volume of a cuboid with a square base and a height of 6 cm if its total surface area is 48 cm². - Fire tank
How deep is the fire tank with the dimensions of the bottom 7 m and 12 m, when filled with 420 m³ of water? - Boxes
Petra has planted flowers in two boxes in the shape of a cube. The first box has an internal dimension of 70 cm and the second 5 dm. She wants to make one box in the shape of a cuboid, into which she could transplant both flowers from these boxes. The new - Longest rod The toolbox has internal dimensions, a length of 1.5 meters, a width of 80 cm, and a height of 6 dm. Calculate the longest rod we can hide in this box.
- Elevation
What must be an observer's elevation so that he may see an object on the Earth 866 km away? Assume the Earth to be a smooth sphere with a radius 6378.1 km. - Road roller
The road roller has a diameter of 1.4 m and a length of 160 cm (a) how many square meters the road rolls when it turns 95 times b) how many times does it turn when rolling a 3 km-long section - The roof
The house's roof has the shape of a regular quadrilateral pyramid 5 m high and the edge of the base 7 m. How many tiles with an area of 540 cm² are needed? - Tin with oil
Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. The canned surface is 1884 cm². Calculate how many liters of oil are in the tin. - The block
The block has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this block.
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