Question

The diameter of a metallic.ball is 4.2 cm. what is the mass of the ball, if the density of the metal is 8.9g per cm3? ​

Answer 1

$\boxed{\mathfrak\purple{Mass \: of \: ball \: is \: 345.39 \: g}}$

Given:

• Diameter of metallic ball = 4.2cm.

To Find:

• Mass of ball = ?

Solution:

Let's first of all find radius of metallic ball,

$\star \: \orange{\underline{\mathfrak{Radius = }}}$

$\\ :\implies\mathfrak{radius = \frac{diameter}{2} } \\ \\ \\ \\ \\ :\implies\mathfrak{radius = \dfrac{\cancel{4.2}}{\cancel{2}}} \\ \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \boxed{:\implies\mathfrak\red{Radius = 2.1cm}}$

We know that;

$\star \: \boxed{\mathfrak\green{Volume \: of \: Sphere \: = \: \frac{4}{3} \pi \: {r}^{3} }}$

Substituting values,

$\\ \\ \\ \\ :\implies\mathfrak{ \frac{4}{3} \times \frac{22}{7} \times ( {2.1)}^{3} } \\ \\ \\ \\ \\ \\ :\implies\mathfrak{ \frac{4}{3} \times \frac{22}{7} \times 9.261} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ :\implies\mathfrak{ \frac{4}{3} \times 22 \times 1.323} \\ \\ \\ \\ :\implies\mathfrak{4 \times 22 \times 0.441} \\ \\ \\ \\ \\ :\implies\mathfrak{88 \times 0.441} \\ \\ \\ \\ \\ \\ \\ \sf\star\underbrace\pink{Volume \: of \: Sphere \: = \: 38.808g} \: \star$

Now,

$:\implies\mathfrak{Density \: of \: metal \: per \: {m}^{3} = 8.9g}$

Placing values,

$:\implies\mathfrak{38.808 \times 8.9} \\ \\ \\ \\ \\ \\ \\ \\ :\implies\mathfrak{345.39} \\ \\ \\ \\ \\ \\ \\ \\ \sf\star \: \underbrace\blue{Density \: of \: metal \: = \: 345.39g} \: \star$

Hence,

• Mass of metallic ball is 345.39g.

Answer 2

$\large{\boxed{\bf{\red{Let's\:understand\:the\:concept\:first!!}}}}$

In this question, the diameter and the density of a metallic ball is given.we need to find the mass of the ball.

To find the mass of the ball we should know the volume of the ball.

$\large\star\:{\underbrace{\sf{\pink{Acknowledgement:}}}}\:\star$

Radius of the sphere = ${\boxed{\sf{\orange{ \dfrac{Diameter}{2}}}}}$

Volume of the sphere = ${\boxed{\sf{\orange{ \dfrac{4}{3} \pi r^{3}}}}}$

Density of the sphere = ${\boxed{\sf{\orange{ \dfrac{Mass}{Volume}}}}}$

$\large\star\:{\underbrace{\sf{\purple{Solution:}}}}\:\star$

Let's find the volume first!!

Radius of the sphere = $\displaystyle{\sf{ \dfrac{4.2}{2} = 2.1cm}}$

Volume of the sphere = $\displaystyle{\sf{ \dfrac{4}{3} \pi r^{3}}}$

• Substituting the values,

$\implies{\sf{ \dfrac{4}{3} \times \dfrac{22}{7} \times (2.1)^{3}}}$

$\implies{\sf{ \dfrac{4}{3} \times \dfrac{22}{7} \times 2.1 \times 2.1 \times 2.1cm^{3}}}$

$\implies{\sf{38.808cm^{3}}}$

${\underline{\sf{\blue{Hence,\:the\:volume\:is\:38.808cm^{3}}}}}$

After that,

Density of the sphere = $\displaystyle{\sf{ \dfrac{Mass}{Volume}}}$

• Substituting the values,

$\implies{\sf{ 8.9g = \dfrac{Mass}{38.808}}}$

$\implies{\sf{ Mass = 38.808 \times 8.9g }}$

$\implies{\sf{ Mass = 345.3912g }}$

${\boxed{\sf{\blue{Hence,the\:mass\:of\:metallic\:ball\:is\:345.39\:(approx.)}}}}$

_____________________