Question

A cow is tethered to a peg fixed at the center of rectangular grass yard 12 m long and 10 m wide with a rope of length 7m. The area of field the cow can graze is

Answer 1

AnswEr :

⋆ Refrence of Image is in the attachment :

• Length of Yard = 12 m
• Breadth of Yard = 10 m
• Length of Rope = Radius = 7 m
• Area of field the Cow can graze is?

If you'll see Cow is tethered at the Centre of Rectangular Grass Yard. Area which Cow can Graze is Area of Circle with Radius 7 m.

• Let's Head to the Question Now :

$\longrightarrow \tt Area \:of \:Circle = \pi r^{2} \\ \\\longrightarrow \tt Area \:of \:Circle =\dfrac{22}{ \cancel{7}} \times \cancel{(7m)^{2}} \\ \\\longrightarrow \tt Area \:of \:Circle =22 \times7{m}^{2} \\ \\\longrightarrow \boxed{ \green{\tt Area \:of \:Circle = 154 \:{m}^{2}}}$

⠀

∴ Cow can graze 154 m² of the field.

$\rule{300}{2}$

• S H O R T C U T ⠀T R I C K :

$\begin{tabular}{|c |c | c|}\cline{1-3}Radius & Circumference & Area \\\cline{1-3}3.5 & 22 & 38.5 \\7 & 44 &154\\10.5 & 66&346.5 \\14 & 88&616\cline{1-2}\cline{1-3}\end{tabular}$

• Simply Memorize this Table, whenever Radius Increases by 3.5

• Circumference will Increase by 22.
• Radius will increase by Square of Increase, i.e. 2 = 4 times, 3 = 9 times

Here Radius of Circle was 7 m, So we got that Cow can graze 154 m² of Field.

#answerwithquality #BAL

Answer 2

$\bf{\Huge{\underline{\boxed{\bf{\green{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\sf{\orange{Given\::}}}}}$

A cow is tethered to a peg fixed at the center of rectangular grass yard 12m long and 10m wide with a rope of length is 7m.

$\bf{\Large{\underline{\sf{\red{To\:find\::}}}}}$

The area of the field the cow can graze.

$\bf{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

$\bf{We\:have\begin{cases}\sf{The\:rectangular\:grass\:yard\:of\:length[l]=12m}\\ \sf{The\:rectangular\;grass\:yard\:of\:breadth[b]=10m}\\ \sf{The\:rope\:of\:length=7m}\end{cases}}$

We know that area of rectangle: (Length × Breadth)   [sq.units]

→ Area of rectangular grass yard = (12 × 10)m²

→ Area of rectangular grass yard = 120m²

According to the question:

We have,

A rope of length = radius of the circle = 7m

We know that formula of the circle: πr²  [sq.units]

→ Area of field = $\bf{(\frac{22}{7} *7*7)m^{2} }$

→ Area of field = $\bf{(\frac{22}{\cancel{7}} *\cancel{7}*7)m^{2} }$

→ Area of field = (22 × 7)m²

→ Area of field = 154m²

Thus,

The area of field the cow can graze is 154m².