Question

the length,breadth,and height of a metal block of mass 160 kg are 50cm,40cm and 20 cm respectively.calculate the density of the metal block.​

Answer 1

$\large \underline{\bf{\orange{Question:-}}}$

The length, breadth and height of a metal block of mass 160kg are 50cm, 40cm and 20cm respectively. Calculate the density of the metal block.

$\large \underline{\bf{\orange{Solution:-}}}$

Here, we are given :

• Length of the metal block = $\sf {\pink{50cm}}$

• Breadth of the metal block = $\sf {\pink{40cm}}$

• Height of the metal block = $\sf {\pink{20cm}}$

• Mass of the metal block = $\sf {\pink{160kg}}$

Firstly, we'll convert the length, breadth and height of the metal block to m from cm.

• $\sf {\pink{Length_{(Block)}:50cm=\dfrac{50}{100}=0.5m }}$

• $\sf {\pink{Breadth_{(Block)}:40cm=\dfrac{40}{100}=0.4m}}$

• $\sf {\pink{Height_{(Block)}:20cm=\dfrac{20}{100}=0.2m}}$

Now, we know that :

$~~~~~~~~\underline{\boxed{\pmb{\mathfrak{\purple{Density=\dfrac{Mass}{Volume}}}}}}$

So, we'll find the volume of the metal block :

$\sf {\blue{:\implies Volume_{(Block)}=LBH}}$

$\sf {\blue{:\implies Volume_{(Block)}=(0.5m)(0.4m)(0.2m)}}$

$\sf {\blue {:\implies Volume_{(Block)} = 0.04m^3}}$

Now, substituting volume and mass in the formula and solving :

$\sf {\green{:\implies Density_{(Block)}=\dfrac{Mass}{Volume}}}$

$\sf {\green{:\implies Density_{(Block)}=\dfrac{160kg}{0.04m^3}}}$

$\sf {\green {:\implies Density_{(Block)} = 4000\dfrac{km}{m^3}}}$

$\pmb{\mathfrak{\purple{\therefore The\; density ~ of~ the ~metal ~block~of~mass}}}\\\pmb{\mathfrak{\purple{160kg~whose~length,~breadth~and~height}}}\\ \pmb{\mathfrak{\purple{are~50cm,~40cm~and~20cm~is~4000km/m^3.}}}$

Answer 2

A N S W E R :

• Density of the metal block is 4000 kg/m³.

Given :

• The length, breadth, and height of a metal block of mass 160kg are 50cm, 40cm and 20cm respectively

To find :

• Find the density of the metal block ?

Solution :

As we know that,

Formula Used :

★ Density = mass/volume

=> Mass = 160kg = 160 × 1000g

=> Volume = 50 × 40 × 20 = 40 × 1000 cm³

=> Density = 160 × 1000/(40 × 100) = 4g³

Or,

=> Mass = 160kg

=> Volume = (50/100) × (40/100) × (20/100) = 4/100m³

=> Density = 160/(4/100) = 4000 kg/m³

Hence,

• Density of the metal block is 4000 kg/m³.