Assam Board Solutions for Chapter: Areas Related to Circles, Exercise 3: Exercise 12.3

The given figure depicts a racing track whose left and right ends are semicircular.

The distance between the two inner parallel line segments is $60 \mathrm{m}$ and they are each $106 \mathrm{m}$ long. If the track is $10 \mathrm{m}$ wide, find the area of the track.

On a square handkerchief, nine circular designs each of radius $7 \mathrm{c}\mathrm{m}$ are made as shown in figure. Find the area of the remaining portion of the handkerchief.

In the given figure, $\mathrm{O}\mathrm{A}\mathrm{C}\mathrm{B}$ is a quadrant of circle with centre $\mathrm{O}$ and radius $3.5 \mathrm{c}\mathrm{m}.$ If  $\mathrm{O}\mathrm{D}=2 \mathrm{c}\mathrm{m},$ find the area of the
Quadrant $\mathrm{O}\mathrm{A}\mathrm{C}\mathrm{B}$

In the given figure, $\mathrm{O}\mathrm{A}\mathrm{C}\mathrm{B}$ is a quadrant of circle with centre $\mathrm{O}$ and radius $3.5 \mathrm{c}\mathrm{m}.$ If $\mathrm{O}\mathrm{D}=2 \mathrm{c}\mathrm{m},$ find the area of the Shaded region.

In the given figure, a square $\mathrm{OABC}$ in inscribed in a quadrant $\mathrm{O}\mathrm{P}\mathrm{B}\mathrm{Q}.$ If $\mathrm{O}\mathrm{A}=20 \mathrm{c}\mathrm{m},$ find the area of the shaded region (use $\pi =\mathrm{}3.14$).

$\mathrm{A}\mathrm{B}$ and $\mathrm{C}\mathrm{D}$ are respectively arcs of two concentric circles of radii $21 \mathrm{c}\mathrm{m}$ and $7 \mathrm{c}\mathrm{m}$ and centre $\mathrm{O}$ as shown in the figure. If $\mathrm{\angle }\mathrm{A}\mathrm{O}\mathrm{B}=30°,$ find the area of the shaded region.
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In the given figure, $\mathrm{ABC}$ is a quadrant of a circle of radius $14 \mathrm{cm}$and a semicircle is drawn with $\mathrm{BC}$ as diameter. Find the area of the shaded region.

Calculate the area of the designed region in the given figure common between the two quadrants of circles of radius $8 \mathrm{c}\mathrm{m}$ each.