Question

Ami has a circular plot of radius 105m. She donates a 7m
boundary for community track.
105m. She donates a 7m wide track along its
a)
Find the area of track
b)
Which mathematical concept is used in the above problem?
c)
By donating a community - track, which value is depicted by Ami?​

Answer 1

(a) Area of track : 4461 m².

(b) Mathematical concept used : Area of circle and area of track.

(c) Value is depicted by Ami : Care for others and society.

To find :

(a) Area of track.

(b) Mathematical concept used.

(c) By donating a community track, which value is depicted by Ami?

Given :

Ami has a circular pot.

Let pot radius be R = 105 m.

She donates a 7 m wide track.

Let wide be 7 m.

She donates a 7 m boundary for community track 105 m.

In-circle radius be r.

From the figure,

Note : Figure is attached below.

Radius ( R ) = OB = R = 105 m

Radius ( r ) = ?

Radius ( r ) = OA = 105 - 7

                        r = 98 m.

(a) To find area of track :

Area of track = $\pi R^2 - \pi r^2$

                      = $\pi ( R^2 - r^2 )$

Using identities $(a^2 - b^2) = (a - b)(a+b)$ we get,

Area of track = $\pi (R - r)(R + r)$

                      = $\pi (105 - 98)(105 + 98)$

                      = $\pi (7)(203)$

                      = $\pi \times 1421$      [ $\pi$ = 3.14 ]

                      = 4461 m².

Therefore, area of track is 4461 m².

(b) Mathematical concept used :

Mathematical concept used is area of circle and area of track.

Area of circle = $\pi r^2$

Area of track = $\pi R^2 -\pi r^2$

(c) Value depicted by Ami :

Ami care for others and also work for society.

To learn more...

1. The ratio of areas of incircle and circumcircle of an equilateral triangle will be ?

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2. The area enclosed between the concentric circles 770cm

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