Question

8. The mass of a spherical ball of radius 2 cm is
8 kg. Find the mass of a spherical shell of the same
material whose inner and outer radii are 4 cm and
5 cm respectively.​

Answer 1

Answer:

Step-by-step explanation:

ANSWER:-

Given that:-

• Mass of a spherical ball 8 kg
• Radius of the ball 2 cm

Second Shell:-

• Re- made spherical shell outer Radii 5 cm
• Inner radii 4 cm

Concept:-

Physics and Maths assemble in this question!

$\sf{Density = \dfrac{Mass}{Volume}}$

Let's Do!

The only catch in this question - Density of both the balls are same, because the material used is same in both ball as well as shell.

Ball Volume (O)

$\sf{Volume \ of \ Ball = \dfrac{4}{3} \pi \times r^3}$

$\sf{Volume \ of \ Ball = \dfrac{4}{3} \times \dfrac{22}{7} \times (2)^3}$

$\sf{Volume \ of \ Ball = 33.52 \ cm^3}$

Density of Ball:-

$\sf{Density = \dfrac{Mass}{Volume}}$

$\sf{Density = \dfrac{8}{33.52}}$ kg/cm^3

Now, volume of shell

= Volume of bigger shell - Volume of smaller shell.

$\sf{Volume \ of \ Shell = \dfrac{4}{3} \pi \times r^3}$

$\sf{Volume \ of \ Shell = \dfrac{4}{3} \times \dfrac{22}{7} \times (5-4)^3}$

$\sf{Volume \ of \ Shell = \dfrac{4}{3} \times \dfrac{22}{7} }$

$\sf{Volume \ of \ Shell = 4.19 \ cm^3}$

Again, we will use:-

$\sf{Density = \dfrac{Mass}{Volume}}$

$\sf{ Mass=Density \times Volume}$

$\sf{Mass = \dfrac{8}{33.52} \times 4.19}$

$\sf{Mass = \dfrac{33.52}{33.52}}$

$\boxed{\sf{Mass = 1 \ kg}}$ is the required answer.

Answer 2

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8. The mass of a spherical ball of radius 2 cm is

8 kg. Find the mass of a spherical shell of the same material whose inner and outer radii are 4 cm and 5 cm respectively.

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$Radius\: of \:the \: spherical \:ball\: is=2cm$

$Mass\:of \:the \:spherical \:ball\:is=8kg$

${ { \underbrace{ \mathbb{ \red{To\:PrOvE\ }}}}}$

$Mass \:of\: the\: spherical \:shell of\\ same\: material$

$Inner\: radii \:is \:4cm$

$Outer\: radii\: is \:5cm$

${ \color{aqua}{ \underbrace{ \underline{ \color{lime}{ \mathbb{\star SoLuTiOn\star }}}}}}$

$\huge \bold{Volume\:of\:ball}$

${\boxed {\frac{4}{3} \pi \times {r}^{3}}}$

$Substitute\: the \:values$

$= \frac{4}{3} \times \frac{22}{7}\times {2}^{3}$

$=33.52 {cm}^{3}$

$\therefore Volume \:of\: the\: ball {\boxed {\boxed {= 33.52{cm}^{3}}}}$

$\huge \bold{Density\: of \:the \:ball}$

${\boxed {Density= \frac{Mass}{Volume}}}$

$Substitute\: the \:values$

${\boxed {\boxed {Density =\frac{8}{33.52} kg/{cm}^{3}}}}$

$\huge\bold{Volume}$

$Volume=Volume \:of\: outer\: shell - volume\\ of\: inner \:shell$

${\boxed {\frac{4}{3} \pi \times {r}^{3}}}$

$Substitute\: the \:values$

$= \frac{4}{3} \times \frac{22}{7}\times {(5-4)}^{3}$

$= \frac{4}{3} \times \frac{22}{7}\times {(1)}^{3}$

${\boxed {\boxed {=4.19{cm}^{3}}}}$

$\therefore Volume \:of \:the \:shell\: is{\boxed {\boxed {=4.19{cm}^{3}}}}$

${\boxed {Density = \frac {Mass}{Volume}}}$

$Mass= Density \times Volume$

$Mass= \frac{8}{33.52} \times 4.19$

$Mass= \cancel \frac{33.52}{33.52}$

${\boxed {\boxed {Mass=1kg}}}$

$\therefore Mass\:of\: the\: spherical \:shell\: is\:{\boxed {\boxed {1kg}}}$

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