Question

Metal A has a density of 55 g/cm3 and metal B has a density of 33 g/cm3 .1200 g of metal A and 600 g of metal B are melted and mixed and then recast into a block.
a) What is the volume of the block?
b) What is the density of the block?

Answer 1

Step-by-step explanation:

Density = mass/volume

given, density of block A is 55g/cm3

mass is given 1200g,

Volume of A in the block = mass/density

1200/55

which is approximately 21.8 cm3.

Density of block B=33g/cm3

mass is given as 600 g

therefore volume = 600/33

it is approximately 18.2 cm3

the volume of the block = volume of A + volume of B

21.8+18.2 = 40 cm3

density = mass/volume

mass=1200+600 =1800

therefore density= 1800/40 =45g/cm3

Hope that helps!

Answer 2

Answer :-

Volume of the block = 39.99 cm³

Density of the block 45.01 g/cm³

Formula used :-

$\tt{\mapsto Density= \dfrac{Mass}{Volume}}$

$\tt{\mapsto Volume= \dfrac{Mass}{Density}}$

Solution :-

✧ Metal A -

Density = 55 g/ cm³

Mass = 1200 g

$\tt{Volume = \dfrac{mass}{Density}}\\\\\tt{=\dfrac{1200\:g}{55\:g}\times cm^{3}}\\\\\tt{=21.81\times cm^{3}}$

✧ Metal B -

Density = 33 g/ cm³

Mass = 600 g

$\tt{Volume = \dfrac{mass}{Density}}\\\\ \tt{=\dfrac{600\:g}{33\:g}\times cm^{3}}\\\\\tt{=18.18\times cm^{3}}$

→ Total Volume of the block

= Volume of metal A + Volume of metal B

= 21.81 cm³ + 18.18 cm³

= 39.99 cm³

→ Total mass of the block

= Mass of metal A + Mass of metal B

= 1200 g + 600 g

= 1800 g

$\tt{\longrightarrow Density\:\:of\:\:the\:\:block = \dfrac{Mass\:\:of\:\:the\:\:block}{Volume\:\:of\:\:the\:\:block }}\\\\\tt{=\dfrac{1800\:g}{39.99\:cm^{3}}=45.01 g/cm^{3}}$

More Information :-

• Density of a body is the measure of Mass of the body for Volume of the body.

• Its SI unit is gram/ centimetre³ or g/cm³.

• It depends upon two factors -

1. Mass of the body
2. Volume of the body

• Formula -

$\tt{\mapsto Density= \dfrac{Mass}{Volume}}$

• More formulas that can be formed from the above mentioned formula are -

$\tt{\mapsto Volume= \dfrac{Mass}{Density}}$

$\tt{\mapsto Mass=Density\times Volume}$