Solid geometry
regular prisms and pyramids (edges), prisms and pyramids: surface area and volume, slant height of a pyramid, space diagonal of a cuboid, units of volume
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Problem
The base of a right prism is an isosceles triangle with two angles of 45°, and its longest side is 3√2 dm long. One side of the rectangle which is the lateral face of this prism with the largest area is 20 dm long. What is the volume of this prism?
Problem
A prism has a right-triangle base with legs 12 cm and 35 cm, and its height is 6 cm. Find its volume.
Problem
A prism with a rectangular base 2 cm by 3 cm has volume 78 cm³. How many centimetres is its height?
Problem
The space diagonal of a cube is 11√3 dm long. What is the volume of this cube?
Problem
Work out the space diagonal of a cuboid with edges 6 cm, 13 cm and 18 cm.
Problem
Convert 22 dm³ to cm³
Problem
A regular square pyramid has a base edge of 12 mm and a lateral edge of 10 mm. What is its lateral surface area?
Problem
A regular square pyramid has a base edge of 12 cm and a lateral edge of 18 cm. What is the total length of all the edges of this pyramid?
Problem
A regular triangular pyramid has a base edge of 2 dm, and the height of each lateral face is 9 dm. What is its lateral surface area?
Problem
A regular triangular prism has a base edge of 4 cm, and its height is 8 cm. What is the total surface area of this prism?
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