© t madas. vertex height base side or lateral face t h e p y r a m i d
TRANSCRIPT
© T Madas
© T Madas
VertexHeight
Base
Side or Lateral Face
1 Base Area Height3
V = ´ ´
T h e P y r a m i d
© T Madas
ExamQuestion
© 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 m1.2 m
30°
x
oppadj
=
0.6x
tanθ
=tan 30°
0.6x =tan 30°
0.6x =tan 30°
x ≈1.03923 m
12
x 0.6x 1.03923A = ≈ 0.3118 m2
A ≈ 0.6236 m2 A ≈ 3.7416 m2
© T Madas
1.2 m
3.7416 m2
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
13
x 3.7416x 2.4V =
= 2.99 m3 [ 3 s.f. ]
© T Madas
ExamQuestion
© T Madas
1.2 m
2.1
m0.6
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 m1.2 m
30°
x
oppadj
=
0.6x
tanθ
=tan 30°
0.6x =tan 30°
0.6x =tan 30°
x ≈1.03923 m
12
x 0.6x 1.03923A = ≈ 0.3118 m2
A ≈ 0.6236 m2 A ≈ 3.7416 m2
© T Madas
3.7416 m2
3.7416 m2
1.2 m
2.1
m0.6
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
3.7416 m2
3.7416 m2
1.2 m
2.1
m0.6
m
Volume of prism= base area x height
Volume of pyramid= 1/3 x base area x height
3.7416x 2.1V1 =
= 7.8574 m3
13
x 3.7416 x 0.6V2 =
= 0.7483 m3
Total Volume = 8.61 m3
[ 3 s.f. ]
© T Madas