Question

in the figure given above AOBC is a quadrant of a circle of radius 10 m. Calculate the area of the shaded portion. Take π= 3.4 and give the answer correct to two significant figures​

Answer 1

Answer:

area of quadrant=πr^2/4

=3.14×10×10/4

=314/4

=78.5 m^2

area of triangle=b×h/2

=10×10/2

=100/2

= 50 m^2

area of shaded region=area of quadrant - area of triangle

=78.5-50

=28.5m^2 is the correct answer

Answer 2

${ \underline{ \underline{\bold{Given}}}}$

Radius, r = 10m,

given value of π = 3.14

${ \underline{ \underline{ \bold{To \: find}}}}$

Area of the shaded region

${ \underline{ \underline{ \bold{Solution}}}}$

Area of shaded region= area of quadrant AOBC - area of ∆ AOB

$= \frac{8}{360} \pi \: {r }^{2} - \frac{1}{2} \times base \times height \\ = \frac{90}{360} \times 3.14 \times 10 \times 10 - \frac{1}{2} \times 10 \times 10 \\ = \frac{314}{4} - 50 \\ = \frac{314 - 200}{4} \\ = \frac{114}{4} \\ = 28.50 {m}^{2}$

Hence, the area of the shaded region is 28.50m².

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