Question

In the figure below RT = 1 cm and OQ = 3 cm.
What is the area of the shaded region?
A. (12.5π – 12) cm2
B. (6.25π – 12) cm2
C. (12.5π – 15) cm2
D. (6.25π – 15) cm2

Answer 1

Answer:

(B)   (6.25π – 12) cm2

Step-by-step explanation:

connect OS which is a radius

now consider triangle ORS

let radius be x so OR = x-1

OS = x

SR=OQ since it is rectangle so SR =3

now by pythagorus theorm , x will be 5 hence radius is 5 cm

now 90/360 * pi * 5 *5 wich is 6.25 pi

this is area of the whole sector

now to find the shaded region we should subtract it by the area of the rectangle which is 12 cm square.. hence problem solved

thank you have a good day and  all the best : )

Answer 2

Ans = B

$(6.25\pi -12)cm^{2}$

Join O and S

And as we know OS is radius

So let Radius OS = OT = x

Therefore, OR = (x-1)

As OT is also radius and RT is given 1cm

OT = OR + RT

OR = (x-1)

By Pythagoras Theorem,

$OS^{2} = OR^{2} + SR^{2} \\x^{2} = (x-1)^{2} +3^{2} \\x^{2} = x^{2}-2x+1 +3^{2}\\2x= 1+9\\x=5$

$x^{2}$ cancelled by $x^{2}$

Now Solve by another answer below or above