Question

a well of diameter 150 cm has 30 cm wide parapet running around it find the area of the parapet
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Answer 1

★ Given:-

The diameter of the well is 150cm.

The well has a 30 cm wide parapet running around it.

★ Solution:-

Diameter of well = 150 cm

Therefore, Radius of well = Diameter÷2 =

$\frac{150}{2}$ =75cm

Width of parapet = 30 cm

Now, the parapet of the well forms two circles.

One is the inner circle and the second one is outer circle.

★ Here:-

Radius of the inner circle = 75 cm

So, radius of outer circle = radius of inner circle + width of parapet

= (75 + 30) cm = 105 cm

We know,

Area of parapet = Area of the outer circle - Area of the inner circle

Therefore, area of the parapet = $πR ^{2}$$− πr ^{2}$

= π($R ^{2} −r ^{2} )$

Therefore, $a ^{2} - b ^{2}$

$= (a+b)(a−b)∣$

$\frac{22}{7} (105+75)(105−75)$

$= \frac{22}{7} \times 180 \times 30$

$= \frac{118800}{7} cm ^{2}$

$=16971.428 \: cm ^{2}$