Question

A crater falls near a village creating a circular pit of diameter 200 m. Find the affected area of land:

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Answer 1

Circle - Mensuration

In order to find the area of the affected land, first we've to find the radius of circular pit. We know that, The radius is half of the diameter. So, we have to divide the diameter value by 2 to get radius of circular pit.

$\rm{\implies Radius = \dfrac{Diameter}{2}} \\ \\ \rm{\implies Radius = \cancel{\dfrac{200}{2}}} \\ \\\rm{\implies \boxed{\textsf{\textbf{Radius = 100}}}}$

Since the circular pit is in the form of Circle shape. So, we will use area of Circle formula here.

We know that, The area of a circle is pi times the radius squared. In Mathematically,

$\implies \rm{ \boxed{ \bf{Area_{(Circle)}= \pi r^2}}}$

Now, by using substituting known values in the formula, we get:

$\rm{ \implies Area_{(Circle)}= \dfrac{22}{7} ({100})^{2} } \\ \\ \rm{ \implies Area_{(Circle)} = \dfrac{22}{7}\times 10000} \\ \\ \rm{ \implies Area_{(Circle)} = \cancel{\dfrac{220000}{7}}}\\ \\ \implies\rm{\boxed{\bf{Area_{(Circle)}=31428.5}}}$

Hence, the area of the affected land is 31428.5m² approximately.

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MORE TO KNOW

• A Circle is a closed plane geometric shape figure.

• The diameter of a circle is the longest chord of a circle.

• The radius drawn perpendicular to the chord bisects the chord.

• A Circle is always lie at an equal distance from a center point.

• Circles having different radius are similar.

• The radius is half of the diameter. i.e. r = D/2.

• The diameter is twice the length of the radius of a circle. i.e. D = 2r.

• The circumference of a circle is the product of pi and length of the diameter of a circle. i.e. C = πD.

• The area of a circle is pi times the radius squared. i.e. A = πr².

Answer 2

Given :

• A crater falls near a village creating a circular pit of diameter 200 m.

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To Find :

• Find the affected area of land.

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Solution :

~ Formula Used :

$\large{\color{blue}{\bigstar \: \: {\underbrace{\underline{\red{\sf{ Area{\tiny_{(Circle) }} = πr²}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

~ Here :

• ➳ ${\sf{π = \dfrac{22}{7}}}$
• ➳ ${{\sf{ R = \cancel\dfrac{200}{2} = 100 \: m}} \bigg\lgroup {\purple{\sf{Radius = \dfrac{Diameter}{2}}}} \bigg\rgroup }$

~ Calculating the Area :

${\longmapsto{\qquad{\rm{ Area{\tiny_{(Circular \: pit)}} = πr² }}}} \\ \\ \ {\longmapsto{\qquad{\rm{ Area{\tiny_{(Circular \: pit)}} = \dfrac{22}{7} \times (100)² }}}} \\ \\ \ {\longmapsto{\qquad{\rm{ Area{\tiny_{(Circular \: pit)}} = \dfrac{22}{7} \times 10000 }}}} \\ \\ \ {\longmapsto{\qquad{\rm{ Area{\tiny_{(Circular \: pit)}} = \cancel\dfrac{22000}{7} }}}} \\ \\ \ {\qquad{\textsf{ Area of Circular pit = {\green{\sf{ 3142.85 \: m² (Approx.) }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

Therefore :

❝ Area of the circular pit caused by the crater is 3142.85 m² (Approx.) .❞

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