Question

.Numerical Problems:

a) A solid ball has a mass of 50 g and volume of 20 cm3


What is its density?


b) A sphere is made from copper whose mass is 3000 kg. If

the density of copper is 8900 kg/m3

, find the volume of

the sphere.


c) A cube with side length 5 m has a density of 4500 kg/m3


What is the mass of the cube?​

Answer 1

Explanation:

1) density=mass/volume

=50/20=2.5

2)volume=density/mass

8900/3000=89/30=2.1

3) mass =density x volume

=5x4500

=22500

Answer 2

Question - 1

Answer :-

Given :-

• Mass of the solid ball = 50 grams

• Volume of a solid ball= 20 cm³

Required to find :-

• Density of the solid ball ?

Formula used :-

$\large \boxed { \tt density = \dfrac{mass}{volume} }$

Solution :-

Given information :-

Mass of the solid ball = 50 grams

Volume of the solid ball = 20 cm³

Using the formula ,

$\boxed { \tt density = \dfrac{mass}{volume} }$

So,

$\rm \: density = \dfrac{50 \: gm}{20 \: {cm}^{3} }$

$\rm density = 2.5 \: g /c {m}^{3}$

Therefore,

Density of the solid ball = 2.5 g/cm³

$\rule{400}{4}$

Question - 2

Answer :-

Given :-

• Mass of the copper sphere = 3000 kg

• Density of the copper sphere = 8900 kg/m³

Required to find :-

• Volume of the sphere ?

Formula used :-

$\large \boxed{ \tt{volume = \frac{Mass}{density} }}$

Solution :-

Given information :-

Mass of the copper sphere = 3000 kg

Density of the copper sphere = 8900 kg/m³

Using the formula,

$\boxed{\tt{ volume = \dfrac{mass}{density} }}$

So,

$\rm volume = \dfrac{3000 \ kg}{8900 \: kg/m^3} \\ \\ \rm volume = \dfrac{30}{89 \; {m}^{3}} \\ \\ \rm volume = 0.33707 \dots \dots \\ \\ \rm volume = 0.337 \: {m}^{3} ( approximately )$

Hence,

Volume of the copper sphere = 0.337 m³ ( approximately )

$\rule{400}{4}$

Question - 3

Answer :-

Given :-

• Side of the cube = 5 meters

• Density of the cube = 4500 kg/m³

Required to find :-

• Mass of the cube ?

Formulae used :-

$\boxed{\tt{ Volume \; of \; a \; cube = {side}^{3}}}$

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

Solution :-

Given information :-

Side of the cube = 5 meters

Density of the cube = 4500 kg/m³

In order to find the mass of the cube we need to find the volume of the cube

So,

Using the formula,

$\boxed{\tt{ Volume \; of \; a \; cube = {side}^{3}}}$

Volume = ( 5 )³

Volume = 125 m³

Using the formula ,

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

Mass = 4500 kg/m³ x 125 m³

m³ get cancelled

Mass = 4500 kg x 125

Mass = 5,62,500 kg

Hence,

Mas of the cube = 5,62,500 kg