PSAT 1.25 Math Diagnostic. What is the area of the shaded sector in square cm?

Math | Passport to Advanced Math |

PSAT | PSAT Math Diagnostic |

PSAT Math | Math Diagnostic |

diagram of a nup side down and twisted icecream cone

circle Why shown in the diagram above has a diameter

of ten centimetres If m equals forty five degrees and

the length of the minor arc x z is ten

thirds pi centimeters What is the area of the shaded

sector in square centimeters and hear the potential answers a

lot of friends So we have a nagging feeling We're

going to have to use our brains on this one

Hope we remember to bring the charger right Let's recap

what we know Looking at the diagram we're told that

the diameter of this circle is ten centimeters which makes

the radius this thing right here Half that or five

centimeters were also told that the measure of the angle

is forty five degrees Him right there And the minor

arc length of x is ten thirds pi centimeters We're

looking for the area of this grayish section over here

So what do we do next Is it time to

use a lifeline waken do this because circles are our

jam We already know that circumference equals diameter times pi

making the circumference of this circle ten pie since the

arc x z is ten thirds pi or one third

of the total length the angle x y z must

be a third of the total angle measurement as well

which is always three hundred sixty degrees when dealing with

the circle one third of three sixty is one twenty

What this also means is that the area of the

unshaded part of the circle is gonna be exactly one

third of the area of the total circle While we

need to do now is find out the area of

the whole circle and then take two thirds of it

to find the area of the shaded portion Unfortunately we've

had the formula for the area of a circle grafted

onto the inside of our islands But we know it's

gonna be pi times are square where are is the

radius The area will be pi times five squared and

five squared is twenty five So the area's twenty five

pie piece of cake Finally you have to take two

thirds of the total area to get shaded portion twenty

five five times two thirds is fifty over three times

pi which is answer c thank very much Xy may

just be a minor arc but we have a feeling

it's gonna make it in the big leagues one day 00:02:13.823 --> [endTime] Maybe it will get to play for the rays