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Pyramids

Pyramids. Information. Pyramids. A pyramid is a polyhedron in which the base is a polygon. It has triangular lateral faces that meet at an apex. The most common pyramids are:. apex. apex. tetrahedron or triangular pyramid. square pyramid. Volume of a pyramid. 1. 3. 1. 3.

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Pyramids

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  1. Pyramids

  2. Information

  3. Pyramids A pyramid is a polyhedron in which the base is a polygon. It has triangular lateral faces that meet at an apex. The most common pyramids are: apex apex tetrahedron or triangular pyramid square pyramid

  4. Volume of a pyramid 1 3 1 3 The volume of a pyramid is found by multiplying the area of its base A by its perpendicular height h and dividing by 3. apex h A base Volume of a pyramid = × area of base × height = Ah

  5. Volume of a pyramid 1 1 1 2 2 3 1 3 What is the volume of this tetrahedron? (hbase)2= 42 + 32 find the height of base: hbase = 5 A =(b× hbase) find the area of base: h = 9cm A = (8 × 5) A = 20cm2 8 cm use the formula for the volume of pyramid: V = Ah 3cm 3cm V = × 20 × 9 V = 60cm3

  6. Surface area of a pyramid 1 1 2 2 Here is the net of a regular tetrahedron. What is its surface area? find the area of each face: A = bh A = × 6cm × 5.2cm A = 15.6cm2 find the surface area SA = 4 × 15.6cm2 5.2cm SA = 62.4cm2 6cm

  7. Volume of a pyramid The Ancient Egyptians built the Pyramids at Giza. The most famous is the Great Pyramid. When it was built, it stood 146.59m high and had square base lengths of 230.33m. What would have been the volume of the original pyramid when it was built? Show your work.

  8. New pyramids

  9. New pyramids The builders need to know how high the pyramids will be so they can order cranes. The cranes can reach: • 54.9 m • 70.1m • 72.2 m • 85.3 m • 91.4 m • 115.8 m. Will these cranes be able to reach the top of the pyramids? h = 3V ÷ A rearrange the formula for volume: height of small pyramid = (37,037m3 × 3) ÷ 2500m2 = 44.4m = (296,296m3 × 3) ÷ 10 000m2 = 88.9m height of medium pyramid height of large pyramid = (1,000,000m3 × 3) ÷ 22 500m2 = 133m

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