Square and Circle area calculation Problem video

[KiteFlyingMe]

HOW COULD I POSIBLY SOLV THIS!!!!....

[8osiris]

w w w.flickr.com /photos /sacred_geometry /5497024890/

This is how you really Square the Circle

[TMalliwuC]

Okay, the answer is not C. Line PR also happens to be the diameter of the circle (4). The area of a Circle is pie times radius squared, thus we halve the diameter to get the radius(2). Pie or 3.14 * 2 *2 = 12.56 - the circles area. Then we do 4*4 (or length times width), to get the area of the square =16. Next, subtract the area of the circle from the area of the square to get - 3.44. 8-2*3.14 = 1.72. But 16-4*3.14 = 3.44. Thus, the answer is D, not C.

[mathproblems]

@TMalliwuC PR is not the diameter of the circle but PS is the diameter of the circle.

PS^2+rs^2=pr^2=4^2=16, BUT PS=PR SO PS^2+PS^2=16 , PS=SQRT(8)

AREA OF THE CIRCLE= PI*8

AREA OF SQUARE=8

SHADED AREA=8-8PI , ANSWER IS C

[mathproblems]

@mathproblems AREA OF THE CIRCLE IS= PI*((SQRT(8))^2)/4 = 2PI

SHADED AREA = 8-2PI WHICH IS THE ANSWER C

[mathproblems]

@TMalliwuC PR IS NOT THE DIAMETER OF THE CIRCLE PS IS THE DIAMETER OF THE CIRCLE VALUE OF PS FROM TRIANGLE PRS CAN BE CALCULATED BY USING PUTHOGOREAN THEOREM PR^2=PS^2+RS^2 4^2=PS^2+RS^2 (SINCE PS=RS) 16=2*PS^2 PS^2=8 PS=SQRT(8) PS=2SQRT(2), RADIUS =SQRT(2) AREA OF CIRCLE-PI*R^2 AREA=PI*2, SQUARE AREA=2SQRT(2)*2SQRT(2)=8 SO SHADED AREA =8-2*PI WHICH IS CHOICE C AND NOT D

[nagu222]

Stupid

Where is the answer?

[Darko2625]

@nagu222 Answer? Are you nuts?

[lnpkural]

Its a simple problem, lol.. Even so many cant resolve it correctly.. The answer is c (8-2pi) Demo : r: Circle radius. Circle area: pi*r*r (pi*R^2) Square surface: (2*r)^2 Shaded area : Square surface - circle area= 4r^2-pi*r^2 = r^2(4-pi) Let's find r.. The sulbasutra formula, a^2+b^2=c^2 (also called Pythagorem's theorem) is applicable here as there are 90 degree angles.. So we have : r^2+r^2=2^2=4 => 2*r^2=4 => r^2=2 => r=sqrt(2) Apply the result..in r^2(4-pi)=asked area

[LTMY]

@lnpkural the last second step of your calculation is wrong. r^2+r^2 DOES NOT EQUAL TO 4, It should be 4^2

[formatguy]

Given: |QP|=|RS|=a |QR|=|PS|=b |PR|=c Let: Shaded Area = A Since: c*c=(a*a)+(b*b) {Since circle: a=b=r} Subsitute & slove for r: c=root(2)r r=[1/root(2)]c Therefore: A = Rectangle(PQRS) - Cricle Subsitute: A = (r*r) - [1/2*(r*r)]PI Simplfy: A = 1/2(c*c) - [(1/8)PI](c*c)

[dooglus]

PR = 4

according to Mr. Pythagorus, PR*PR = PS*PS + SR*SR

ie. 4*4 = PS*PS + PS*PS (since PS = SR - it's a square)

ie. 2PS*PS = 16; PS*PS = 8; PS=2*root(2)

so the radius of the circle is root(2), and the side of the square is 2*root(2)

shaded area = area(square) - area(circle)

= 2*root(2) * 2*root(2) - pi*root(2)*root(2)

= 4*2 - 2*pi

= 8 - 2*pi

[titanas2]

it is a B) 100%

8-pi*r^2 = 8-4pi , coz r=2sqrt^2/2

[NidhiS]

i hv checked it so many times but still can't figure out the problem

[mathproblems]

what is the area of the square?

[NidhiS]

area of square =a*a  = 2(2^1/2)*2(2^1/2) =8

[mathproblems]

I am sorry yuo are correct I was wrong

[mathproblems]

tha answer is (8-2pi) C

[NidhiS]

i did it like this: let the side of the square be a so PR=[(2a*a)^1/2] ie 4= a*[(2)^1/2] ie a=2(2^1/2) area of square=a*a  =8 now area of circle =pi*r*r r=a/2 so r=(2^1/2) therefore area of circle=pi*2 area of shaded region= 8-2pi

[NidhiS]

I think the answer is C

[TheChosenUno]

Is it c? Took me about 1 1/2 min

[MrMiyagii]

Hmm... hard

[ThePen0rMaster]

The answer is A.

[marjan15]

(D) 16-4Pi

It took me about 1 minute.

[mathproblems]

Incorrect answer