Question

a square of side 14cm is cut from a quadrant OPBQ of a ciecle with centre O. Find the area of the shaded region.

Answer 1

Area of the shaded region is given by,

$\displaystyle\longrightarrow\sf{A=Area(OPBQ)-Area(OABC)\quad\quad\dots(1)}$

OPBQ is actually a quarter circle, or a quadrant, whose radius is,

$\displaystyle\longrightarrow\sf{r=OB}$

Well, OB is the diagonal of the square OABC of side 14 cm. Thus,

$\displaystyle\longrightarrow\sf{r=OB=14\sqrt{2}\ cm}$

Hence area of OPBQ is,

$\displaystyle\longrightarrow\sf{Area(OPBQ)=\pi\left(14\sqrt2\right)^2}$

$\displaystyle\longrightarrow\sf{Area(OPBQ)=392\pi\ cm^2}$

The area of the square OABC is,

$\displaystyle\longrightarrow\sf{Area(OABC)=14^2=196\ cm^2}$

Then, in (1),

$\displaystyle\longrightarrow\sf{A=392\pi-196}$

$\displaystyle\longrightarrow\sf{\underline{\underline{A=196(2\pi-1)\ cm^2}}}$

If $\displaystyle\sf{\pi}$ is taken as $\displaystyle\sf{3.14,}$

$\displaystyle\longrightarrow\sf{A=196(2\times3.14-1)}$

$\displaystyle\longrightarrow\sf{\underline{\underline{A=1034.88\ cm^2}}}$

Answer 2

Answer:

area of the shaded reign is 154cm² .

Step-by-step explanation:

area of shaded reign = area of - area of

quadrant. square.

= 1/4 πr². - a²

= 1/4 22/7(14√2)² - 14²

= 1/2 11/7 × 392 - 196

= 1/2 11/7 × 196

= 1/2 × 308

= 154cm²......

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