Question

A road that is 7 m wide surrounds a circular path whose circumference is 352 m. what will be the area of the road?

Answer 1

GIVEN

A road width is 7 m.
Circumference of circular path = 352 m
r = radius of circular path.
pi = 22 / 7
Therefore, 2 pi r = 352
r = 352 / 2 pi
r = 176 / pi
r = (176 x 7) / 22
r = 8 x 7
r = 56 m
Therefore, diameter of circular path
= 2 x 56
= 112 m
As diameter of circular path is equal to the length of the road.
Therefore, length of the road = 112 m
A road width is 7 m. (as given)
Area of road = length x width
= 112 x 7
= 784 m^2.

Answer 2

Let the radius of the park be r m

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$\:\:\:\:\:\:\:\:\:\:$Then, its circumference = 2πr

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mapsto\:$ $\sf\bold 2\pi r=352$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mapsto\:$$\sf 2×\bf\dfrac{22}{7}×r=352$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mapsto\:$$\sf r=\bigg(352×\bf\dfrac{7}{44}\bigg)=56$

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Thus,

• $\sf\bold Inner\: radius = 56 m,$
• $\sf\bold Outer \:radius = (56+7)=63m.$

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$\sf \:\:\:\:Area\: of\: the\: road\: = \:\pi[(63)²-(56)²]m²$

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$\sf \:\:\:\:\:\:\:\:\:=\:\bf\dfrac{22}{7}×(63+56)(63-56)m²$

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$\sf \:\:\:\:\:\:=\:\bigg(\bf\dfrac{22}{7}×119×7\bigg)m²=2618m²$

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$\:\:\:\:\:\:\:\:─────────────────────$

${\large{\frak{\pmb{\underline{Related\: points \:and \:formulas}}}}}$

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Circle}}}}$

The set of points which are at a constant distance of r units from a fixed point O is called a circle with centre O and radius = r units.

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Circumference}}}}$

• The perimeter (or length of boundary) of a circle is called its circumference.

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Radius}}}}$

• A line segment joining the centre of a circle and a point on the circle is called radius of the circle.

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Chord}}}}$

• A line segment joining any two points on a circle is called a chord of the circle.

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Diameter}}}}$

• A chord of a circle passing through its centre is called a diameter of the circle.

$\:\:\:$$\small\green{ \large\star}$Diameter is the longest chord of the circle.

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$$\underline{\boxed{\sf{Diameter=\frak{\red{2×radius}}}}}$

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Secant}}}}$

• A line which intersects a circle at two points is called a secant of a circle.

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Arc}}}}$

• A continuous piece of a circle is called an Arc of the circle.

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Central\:Angle}}}}$

• An angle subtended by an Arc at the centre of a circle is called its Central angle.

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Semicircle}}}}$

• A diameter divides circle into two equal arcs. Each of these arcs is called a semicircle.

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$\underline{\underline{\maltese\:\: \textbf{\textsf{Quadrant}}}}$

• One fourth of a circle disc is called a quadrant.

$\:\:\:$$\small\blue{ \large\star}$The central angle of quadrant is 90°

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F O R M U L A E,

$\orange\longrightarrow$$\sf Circumference\: of\: the \:circle =2\pi r$

$\pink\longrightarrow$$\sf Area\: of \:the \:circle=\pi r²\:\:\:\:or\:\:\:\bf\dfrac{\pi d²}{4}$

$\purple\longrightarrow$$\sf Area\: of \:the \:semicircle=\dfrac{1}{2}\pi r²$

$\red\longrightarrow$$\sf Perimeter \:of \:the\: semicircle=(\pi r+2r)$