Question

Ashish is digging a pit of radius 2.8 m and 3 m
depth. He is using the mud dug out from the pit to
fill a vacant area of land of dimensions 8 mx 2 m.
Find the raised height of the vacant area.​

Answer 1

AnswEr :

${\underline {\boxed { \purple{ \rm 4.62 \: m}}}}$

Given :

• Radius is 2.8.

• Depth is 3 m.

• He's using the mud dug out from the pit to fill a vacant area of land of dimensions 8 m × 2 m.

To Find :

• The raised height of the vacant area.

Calculation :

So, first of all let's calculate the volume of the pit.

Formula to be used :

• ${\underline {\boxed {\pmb { {Volume}_{(of \: pit)} = \pi \: r^2 \: h} }}}$

$\dag$ Putting the values,

$\longrightarrow \sf \: \dfrac{22}{7} \: \times 2.8 \times 2.8 \times 3 \\ \\ \\ \longrightarrow \sf \large{ \boxed{ \blue{ \frak{73.92^3}}}}$

Therefore, Volume of pit is $\rm{ \red{73.92^3}}$.

$\dag \: { \underline {\boldsymbol {According \: to \: the \: Question,}}}$

Let's calculate the raised height of the vacant area.

Henceforth,

• Total area of the land = Total volume of the spit

Where,

• Total Area of land = 8 m × 2 m = 16 m
• Total Volume of the spit = $\rm \: 73.92^3$

$\longrightarrow{ \red {\sf \: Height = \dfrac{Area}{Volume}}} \\ \\ \\ \longrightarrow \sf \: Height = \cancel\dfrac{73.92}{16} \\ \\ \\ \longrightarrow \boxed{ \purple{ \sf \: Height = 4.62 \: m}} \star$

Therefore, the raised height of the vacant area is ${ \red{ \rm{4.62 \: m}}}$.

Answer 2

Given :-

• Radius is 2.8.
• Depth is 3m.
• He's using the mud dug out from the pit to fill a vacant area of land of dimensions 8 m × 2m.

To find :-

• The raised height of the vacant area.

Solution :-

So, first of all let's calculate the value of the pit.

Formula Used :

• ${\underline {\boxed {\red {\rm {voume_{(of \: pit)} = π {r}^{2} h}}}}}$

$\large\dag$ Putting the values :

$\large\implies$ $\large{\rm{\frac{22}{7} \times 2.8 \times 2.8 \times 3}}$

$\: \: \: \: \: \:$

$\: \: \: \:$ $\boxed{\rm\underline\green{73.92³}}$ ${\bf\red{★}}$

Therefore,

• Volume of pit is ${\sf\underline\green{73.92³}}$

★ According to the question

Let's calculate the raised height of the vacant area.

Henceforth,

• Total area of the land = Total volume of the spit.

Where,

• Total Area of land = 8m × 2m = 16m
• Total Volume of the spit = 73.92³.

$\large\rightarrow$ $\large{\sf{Height = \frac{Area}{Volume}}}$

$\: \: \: \:$

$\large\rightarrow$ Height = $\dfrac{\cancel{73.92}}{\cancel{16}}$

$\: \: \: \:$

$\large\rightarrow$ $\boxed{\sf\underline\blue{Height = 4.62 m}}$★

Hence,

• Therefore, the raised height of the vacant area is 4.62 m. $\large{\bf\green{✓}}$