Answer:
Density of steel = 80.73 gm/[tex]cm^3[/tex]
Step-by-step explanation:
The figure is made up of cuboid and square pyramid.
Height of cuboid, h = 9 cm
Length of cuboid, l = 6 cm
Width of cuboid, w = 6 cm
Volume of cuboid is given by the formula:
[tex]V_{Cuboid} = l \times w \times h[/tex]
[tex]V_{Cuboid} = 6 \times 6 \times 9\\\Rightarrow V_{Cuboid} = 324\ cm^3[/tex]
Density of Wood , [tex]D_{Cuboid}[/tex]= 0.68g/[tex]cm^3[/tex]
We know that formula of Density is:
[tex]Density = \dfrac{Weight}{Volume}[/tex]
[tex]D_{Cuboid} = \dfrac{W_{Cuboid}}{V_{Cuboid}}\\\Rightarrow W_{Cuboid} = V_{Cuboid} \times D_{Cuboid}[/tex]
Putting the values:
[tex]W_{Cuboid} = 324 \times 0.68 = 220.32\ gm[/tex]
Total weight = [tex]W_{Cuboid} + W_{Pyramid}[/tex]
970 = 220.32 [tex]+ W_{Pyramid}[/tex]
[tex]W_{Pyramid}[/tex] = 749.68 gm
Volume of pyramid is given as:
[tex]V_{Pyramid}= \dfrac{1}{3} \times \text{Area of Base} \times \text{Vertical Height}[/tex]
Base is a square with side 6 cm
[tex]V_{Pyramid}= \dfrac{1}{3} \times 6 \times 6 \times (17 -9)\\V_{Pyramid}= 96\ cm^3[/tex]
Density of Steel/Pyramid:
[tex]D_{Pyramid} = \dfrac{W_{Pyramid}}{V_{Pyramid}}\\\Rightarrow D_{Pyramid} = \dfrac{749.68}{96}\\\Rightarrow D_{Pyramid} = 80.73\ gm/cm^3[/tex]
