© T Madas. Vertex Height Base Side or Lateral Face T h e P y r a m i d.

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Presentation transcript:

© T Madas

Vertex Height Base Side or Lateral Face T h e P y r a m i d

© T Madas Exam Question

© T Madas 1.2 m 2.4 m A pyramid has a base in the shape of a regular hexagon. The hexagonal base has a side length of 1.2 m. The height of the pyramid is 2.4 m. Calculate the volume of the pyramid correct to 3 significant figures.

© T Madas 0.6 m 1.2 m 30° x opp adj = 0.6 x tanθ = tan 30° 0.6x = tan 30° 0.6 x = tan 30° x ≈ m 1 2 x 0.6 x A =A = ≈ m 2 A ≈ m 2 A ≈ m 2 c c c c

© T Madas 1.2 m m m A pyramid has a base in the shape of a regular hexagon. The hexagonal base has a side length of 1.2 m. The height of the pyramid is 2.4 m. Calculate the volume of the pyramid correct to 3 significant figures. Volume of pyramid = 1 / 3 x base area x height 1 3 x x 2.4 V =V = = 2.99 m 3 [ 3 s.f. ]

© T Madas Exam Question

1.2 m 2.1 m 0.6 m A conservatory has the shape of a pyramid on top of a prism. The base of the prism and the base of the pyramid are regular hexagons of side length 1.2 m. The height of the prism is 2.1 m and the height of the pyramid is 0.6 m. Calculate the volume of the conservatory correct to 3 significant figures.

© T Madas 0.6 m 1.2 m 30° x opp adj = 0.6 x tanθ = tan 30° 0.6x = tan 30° 0.6 x = tan 30° x ≈ m 1 2 x 0.6 x A =A = ≈ m 2 A ≈ m 2 A ≈ m 2 c c c c

© T Madas m m 2.1 m 0.6 m A conservatory has the shape of a pyramid on top of a prism. The base of the prism and the base of the pyramid are regular hexagons of side length 1.2 m. The height of the prism is 2.1 m and the height of the pyramid is 0.6 m. Calculate the volume of the conservatory correct to 3 significant figures.

© T Madas m m 2.1 m 0.6 m Volume of prism = base area x height Volume of pyramid = 1 / 3 x base area x height x 2.1 V1 =V1 = = m x x 0.6 V2 =V2 = = m 3 Total Volume = 8.61 m 3 [ 3 s.f. ]

© T Madas