Question

In a circular plot of land 70mt. in diameter has a path 7mt. wide running outside it. Find the area of the
path.
​

Answer 1

Answer:

Diameter of grassy plot = 70 m

Radius of grassy plot =

We are given that a circular grassy plot has a path 7 M wide running around it on the outside

Outer radius = 35 m + 7 m= 42 m

Area of path = Outer area - inner area

Area of path =

Area of path =

Area of path = 1694 sq.m.

Cost of graveling 1 sq.m. = Rs.4

Cost of graveling 1694 sq.m. =

Hence the cost of gravelling the path is Rs.6776

Answer 2

The area of the circular path is 1694 m².

Given:

• A circular plot of land 70m in diameter.
• Has a path 7m wide running outside it.

To find:

• Find the area of the path.

Solution:

Formula to be used:

$\text{\bf Area of path}\bf =\pi( {R}^{2} - {r}^{2} )$

Here, R: radius of large/outer circle

r: radius of small/inner circle.

Step 1:

Write the values to be used in formula.

As,

Diameter of circular land (D)= 70 meter

$\bf Radius (r)= \frac{Diameter}{2}$

$r = \frac{70}{2}$

$\bf r = 35 \: m$

Radius of outer circle/including path:

Since path is 7 m wide.

So,

$R = 35 + 7$

$\bf R = 42 \: m$

Step 2:

Find the area of path.

$\text{Area of path} = \frac{22}{7} ( ({42})^{2} - ({35})^{2} )$

$\text{Area of path} = \frac{22}{7} ( 1764 - 1225)$

$\text{Area of path} = \frac{22}{7} \times 539$

$\text{Area of path} = 22 \times 77$

$\text{\bf Area of path} \bf = 1694 \: {m}^{2}$

Thus,

Area of circular path is 1694 m².

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