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

3. © T Madas Exam Question

4. © 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.

5. © 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 ≈ 1.03923 m 1 2 x 0.6 x 1.03923 A =A = ≈ 0.3118 m 2 A ≈ 0.6236 m 2 A ≈ 3.7416 m 2 c c c c

6. © T Madas 1.2 m 3.7416 m 2 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. Volume of pyramid = 1 / 3 x base area x height 1 3 x 3.7416 x 2.4 V =V = = 2.99 m 3 [ 3 s.f. ]

7. © T Madas Exam Question

8. 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.

9. © 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 ≈ 1.03923 m 1 2 x 0.6 x 1.03923 A =A = ≈ 0.3118 m 2 A ≈ 0.6236 m 2 A ≈ 3.7416 m 2 c c c c

10. © T Madas 3.7416 m 2 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.

11. © T Madas 3.7416 m 2 1.2 m 2.1 m 0.6 m Volume of prism = base area x height Volume of pyramid = 1 / 3 x base area x height 3.7416 x 2.1 V1 =V1 = = 7.8574 m 3 1 3 x 3.7416 x 0.6 V2 =V2 = = 0.7483 m 3 Total Volume = 8.61 m 3 [ 3 s.f. ]

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