Solid geometry
relative position of lines in a cube, diagonal of a cuboid and its angle with the base, volume of prisms and pyramids, surface area and volume of regular prisms and pyramids, angles in pyramids, surface area and volume of cylinders, cones and spheres, angles in cones and cylinders, similar solids
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Find the ratio of the volume of the first solid to that of the second, as a fraction
The surface areas of two similar solids are in the ratio 25 : 16 (the area of the first to the area of the second).
Find the volume of the prism
A regular square prism has a base edge of 5 cm, and its diagonal makes an angle of 45° with the plane of the base.
Compute the length of the diagonal of the cuboid
A cuboid has edges of 3 cm, 16 cm and 5 cm.
Compute the tangent of the angle between the diagonal of the solid and the base
A cuboid has a square base with side 7 cm and a height of 27 cm.
Compute the volume of the solid
Two similar solids have their edges in the ratio 7 : 2. The volume of the first one is 343 cm³. What is it for the second one?
Are the lines CF and EH perpendicular?
The figure shows the cube ABCDEFGH (ABCD is the lower base, and E, F, G, H lie above A, B, C, D).
Compute the volume of the pyramid
A regular square pyramid has a base edge of 16 cm and a height of 6 cm.
Compute the surface area of the sphere
A sphere has a diameter of 24 dm.
Compute the total surface area
A cylinder has a base radius of 9 cm and a height of 11 cm.
Compute the height of the pyramid
A regular square pyramid has a base edge of 8 cm, and its lateral faces make an angle of 45° with the plane of the base.
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