Question

A hollow spherical shell is made of a metal of density 4.5 gm per cubic cm. If it’s

external and internal radii are 9 cm and 8 cm respectively, find the weight of the

shell​

Answer 1

${\underline {\sf \blue{ Question }}}$

• A hollow spherical shell is made of a metal of density 4.5 gm per cubic cm. If it’s external and internal radii are 9 cm and 8 cm respectively, find the weight of the shell.

${\underline {\sf {\orange{Answer}}}}$

• The weight of spherical shell = 4.092kg
• The volume of spherical shell = 909.33

${\underline {\sf \green{Given}}}$

• Density of hollow spherical shell is 4.5 gm per cubic cm.
• Internal radii = 8cm
• External radii = 9cm

${\underline {\sf \purple{To \: Calcutate}}}$

• The weight of the shell.

${\underline {\sf \orange{Explanation}}}$

Let the internal radii of spherical shell be R = 9cm

Let the external radii of spherical shell be r = 8cm

${\underline {\sf \green{According \: to \: the \: question}}}$

Case I

$\sf Volume \: of \: spherical \: shell \: v = \frac{4}{3} \pi ( {R}^{3} \times {r}^{3} )$

$\sf Volume = \frac{4}{3} \times \frac{22}{7} ( {9}^{3} \times {8}^{3} )$

Then,

$\implies \: \sf\frac{8 \times 22}{3 \times 7} (729 - 512)$

$\implies \: \sf \frac{88}{21} \times 217$

Now,

$\implies \sf \: \frac{19096}{21}$

$\implies \sf \: 909.33$

Case II

Weight of 1 cubic cm = 4.5gm

So,

The weight of spherical shell = 4.5 × 909.33

Weight of spherical shell = 4092 grams/4.092kg

${\underline {\sf \red{ Hence }}}$

• The weight of spherical shell = 4092 grams/4.092kg

Answer 2

Question:-

1. A hollow spherical shell is made of a metal of density 4.5 gm per cubic cm. If it’s  external and internal radii are 9 cm and 8 cm respectively, find the weight of the  shell?​

To find,

• The weight of the shell

Given that:-

• Density = 4.5 gm
• External radii = 9 cm
• Internal radii = 8cm

Solution:-

Internal radius = 8cm

External radius = 9cm

Volume = external - internal                     $\rm V =\dfrac{4}{3}\pi r^{2}$

$\rm =>\dfrac{4}{3}\pi (4)^{3}-\dfrac{4}{3}\pi (8)^{3}$

$\rm => \dfrac{4}{3}\pi \:( 9^{3}-8^{3})=\dfrac{4}{3}\pi (729-512)$

$\rm => \dfrac{4}{3} \times \pi \times 217=908.96 \: cm^{3}(\pi =3.14)$

$\rm =>\dfrac{4}{3} \times \dfrac{22}{7} \times 217$

$\rm => 909.33 \: or \: (\dfrac{2728}{3})cm^{3}$

$\rm => M = V \times D=\dfrac{2728}{3} \times 4.5$

                       = 4092 g

4092 when converted into kg is 4.092 kg