Question

The density of an object with Mass=10g and Volume=100 cubic cm

Answer 1

GIVEN :-

• Mass of an object = 10g
• Volume of the object = 100 cubic cm

TO FIND :-

• Density of the object

SOLUTION :-

We have ,

• Mass = 10g
• Volume = 100 cm³

Relation between Mass , Volume and density is given by ,

$\large {\underline{\boxed {\red{ \bf{density = \frac{mass}{volume} }}}}}$

$\implies \bf \: density = \frac{10g}{100 \: cm {}^{3} } \\ \\ \implies \bf \: density = \frac{ 1\cancel{0}}{1 \cancel{00}} \\ \\ \implies {\underline {\boxed {\blue {\bf{density = 0.1 \: gcm {}^{ - 3} }}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(OR)

We have ,

• Mass = 10g = 0.01 kg
• Volume = 100 cm³ = 100 × 10⁻⁶ m³ = 10⁻⁴ m³

Since ,

$\large {\underline{\boxed {\red{ \bf{1g = 0.0001 \: kg }}}}}$

$\large {\underline{\boxed {\red{ \bf{1cm {}^{3} = 1 \times {10}^{ - 6} \: {m}^{3} }}}}}$

$\implies \bf \: density = \frac{0.01 \: kg}{0.0001 \: m {}^{3} } \\ \\ \implies \bf \: density = \frac{ {10}^{ - 2} \: kg}{ {10}^{ - 4} \: {m}^{3} } \\ \\ \implies \bf \: density = {10}^{ - 2} \times {10}^{ 4} \: kg.m {}^{ - 3} \\ \\ \implies \bf \: density = {10}^{2} kg. {m}^{ - 3} \\ \\ \implies {\underline{ \boxed {\blue {\bf{density = 100 \: kg. {m}^{ - 3} }}}}}$

∴ The density of the given object is 0.1 g/cm³ (or) 100 kg/m³

Answer 2

Answer:

GIVEN :-

Mass of an object = 10g

Volume of the object = 100 cubic cm

TO FIND :-

Density of the object

SOLUTION :-

We have ,

Mass = 10g

Volume = 100 cm³

Relation between Mass , Volume and density is given by ,

\large {\underline{\boxed {\red{ \bf{density = \frac{mass}{volume} }}}}}

density=

volume

mass

\begin{gathered} \implies \bf \: density = \frac{10g}{100 \: cm {}^{3} } \\ \\ \implies \bf \: density = \frac{ 1\cancel{0}}{1 \cancel{00}} \\ \\ \implies {\underline {\boxed {\blue {\bf{density = 0.1 \: gcm {}^{ - 3} }}}}}\end{gathered}

⟹density=

100cm

3

10g

⟹density=

1

00

1

0

⟹

density=0.1gcm

−3

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(OR)

We have ,

Mass = 10g = 0.01 kg

Volume = 100 cm³ = 100 × 10⁻⁶ m³ = 10⁻⁴ m³

Since ,

\large {\underline{\boxed {\red{ \bf{1g = 0.0001 \: kg }}}}}

1g=0.0001kg

\large {\underline{\boxed {\red{ \bf{1cm {}^{3} = 1 \times {10}^{ - 6} \: {m}^{3} }}}}}

1cm

3

=1×10

−6

m

3

\begin{gathered} \implies \bf \: density = \frac{0.01 \: kg}{0.0001 \: m {}^{3} } \\ \\ \implies \bf \: density = \frac{ {10}^{ - 2} \: kg}{ {10}^{ - 4} \: {m}^{3} } \\ \\ \implies \bf \: density = {10}^{ - 2} \times {10}^{ 4} \: kg.m {}^{ - 3} \\ \\ \implies \bf \: density = {10}^{2} kg. {m}^{ - 3} \\ \\ \implies {\underline{ \boxed {\blue {\bf{density = 100 \: kg. {m}^{ - 3} }}}}}\end{gathered}

⟹density=

0.0001m

3

0.01kg

⟹density=

10

−4

m

3

10

−2

kg

⟹density=10

−2

×10

4

kg.m

−3

⟹density=10

2

kg.m

−3

⟹

density=100kg.m

−3

∴ The density of the given object is 0.1 g/cm³ (or) 100 kg/m³