Question

A shot putt is a metallic sphere of radius 4.9cm. If the density of the metal is 7.8 per cm^3. Find the mass of the shot putt.

Answer 1

$\huge{\underline{\underline{\mathrm{\blue{GIVEN:-}}}}}$

• Radius of metallic sphere = 4.9 cm
• Density of metal = 7.8 g/cm³

$\huge{\underline{\underline{\mathrm{\blue{NEED\:TO\:FIND:-}}}}}$

What is the mass of the shot putt = ?

$\huge{\underline{\underline{\mathrm{\blue{FORMULA \:USED:-}}}}}$

$\bf\red{Volume \:of\: sphere = \frac{4}{3}\timesπ{r}^{3}}$

$\bf\red{Mass = Density \:\times\: Volume}$

$\huge{\underline{\underline{\mathrm{\blue{SOLUTION:-}}}}}$

∴ Firstly, we need to find the volume

Putting the given values in formula, we get

$\implies$ $\bf{\frac{4}{3} \times\frac{22}{7 }\times{ (4.9)}^{3}}$

$\implies$$\bf{\frac{4}{3}\times{22}{7} \times4.9 \times 4.9 \times 4.9 }$

$\implies$$\bf{\frac{88}{21}\times117.649}$

$\implies$$\cancel\dfrac{10353.112}{21}$

$\large\bf\green{Volume = 493\: {cm}^{3}approx.}$

∴ Now, we have to find the mass of metal

$\bf\red{Mass = Density \times Volume}$

$\implies$$\bf{Mass = 7.8 \times 493}$

$\large\bf\green{ Mass = 3845.4\: g }$

Convert g into kg

$\implies$$\rm{ 1\: kg = 1000\: g}$

$\implies$$\rm{\frac{3845.4}{1000} = 3.8454\: kg}$

$\large{\underline{\underline{\mathrm{\blue{FINAL\:ANSWER:-}}}}}$

$\huge{\boxed{\boxed{\mathrm{\green{Mass = 3.8454 \:kg}}}}}$

Answer 2

Given:

Radius of sphere = 4.9cm

Density of metal = 7.8g/cm³

Formula used;

Vol of sphere = 4/3 × πr³

Mass = density × vol

Solutions:

4/3 × 22/7 × (4.9)³

4/3 × 22/7 × 4.9 × 4.9 × 4.9

88/21 × 117.649

10353.112/21

493cm³

Vol = 493cm³

Mass = Density × Vol

M = 7.8 × 493

M = 3845.4g

M = 3.8454kg

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