Solid geometry, stereometry - page 85 of 121
Number of problems found: 2409
- 4B - truncated pyramid
Calculate the volume of a regular truncated quadrilateral pyramid if the base edges are 10cm and 4cm and the height of the side wall is 5cm. - Pyramid edge calculation
The foundations of a regular truncated quadrilateral pyramid are squares. The lengths of the sides differ by 6 dm. Body height is 7 dm. The body volume is 1813 dm³. Calculate the lengths of the edges of both bases. - Axial section
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm square. Calculate the radius of the base. - Cylinder volume diagonal
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. - Cone surface volume
Calculate the cone's surface and volume if its base diameter is 1 dm and the side length is 13 cm. - Pool capacity
The pool is 30 m long, 12 m wide, and 2 m deep. Can it contain 7,000 hl of water? If so, what is the level? If not, how much extra water is there? - Hexagonal prism 2
The regular hexagonal prism has a surface of 140 cm² and a height of 5 cm. Calculate its volume. - Cuboid
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges. - Suitcase - rod
The trunk of a car has the shape of a cuboid with sides 1.6m x 1.2m x 0.5m (width, depth, height). Determine the longest thin rod that can be placed on the bottom. - Spherical segment
Calculate the volume of the spherical segment and the surface area of the canopy if the radius of the sphere is r = 5 cm and the radius of the circular base of the segment ρ = 4 cm. - A plane vs. sphere
The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere. - Wallpaper
3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper if he has a roll of wallpaper 50 cm wide? - Block volume calculation
The surface of the block is 558 cm², and its dimensions are in the ratio of 5:3:2. Calculate the volume. - Pyramid surface calculation
Calculate the surface area of a regular quadrilateral pyramid given: a= 3.2 cm h= 19 cm Method: 1) calculation of the height of the side wall 2) area of the base 3) shell areas 4) the surface of a regular quadrilateral pyramid - Cube measurements
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Cube 5
The surface of the cube is 15.36 dm². How will this cube's surface area change if the edges' length is reduced by 2 cm? - Floating barrel
The barrel (cylinder shape) floats on water, the top of the barrel is 18 dm above water, and the width of the surfaced barrel part is 34 dm. The barrel length is 12 dm. Calculate the volume of the barrel. - Axial cut
The cone surface is 388.84 cm2, and the axial cut is an equilateral triangle. Find the cone volume. - Cube edge surface
The length of the cube's edge in cm is expressed as a natural number. Its volume is greater than 100 and less than 200. Calculate the surface area of the cube.
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