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harkovskaia [24]
3 years ago
8

The object on the right is made from a square-based pyramid joined to a cuboid.

Mathematics
1 answer:
spayn [35]3 years ago
5 0

Answer:

Density of steel = 80.73 gm/cm^3

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:

V_{Cuboid} = l \times w \times h

V_{Cuboid} = 6 \times 6 \times 9\\\Rightarrow V_{Cuboid} = 324\ cm^3

Density of Wood , D_{Cuboid}= 0.68g/cm^3

We know that formula of Density is:

Density = \dfrac{Weight}{Volume}

D_{Cuboid} = \dfrac{W_{Cuboid}}{V_{Cuboid}}\\\Rightarrow W_{Cuboid} = V_{Cuboid} \times D_{Cuboid}

Putting the values:

W_{Cuboid} = 324 \times 0.68 = 220.32\ gm

Total weight = W_{Cuboid} + W_{Pyramid}

970 = 220.32 + W_{Pyramid}

W_{Pyramid} = 749.68 gm

Volume of pyramid is given as:

V_{Pyramid}= \dfrac{1}{3} \times \text{Area of Base} \times \text{Vertical Height}

Base is a square with side 6 cm

V_{Pyramid}= \dfrac{1}{3} \times 6 \times 6 \times (17 -9)\\V_{Pyramid}= 96\ cm^3

Density of Steel/Pyramid:

D_{Pyramid} = \dfrac{W_{Pyramid}}{V_{Pyramid}}\\\Rightarrow D_{Pyramid} = \dfrac{749.68}{96}\\\Rightarrow D_{Pyramid} = 80.73\ gm/cm^3

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