# PSAT 1.25 Math Diagnostic

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

### Transcript

00:15

diagram of a nup side down and twisted icecream cone

00:18

circle Why shown in the diagram above has a diameter

00:21

of ten centimetres If m equals forty five degrees and

00:24

the length of the minor arc x z is ten

00:27

thirds pi centimeters What is the area of the shaded

00:31

sector in square centimeters and hear the potential answers a

00:35

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

00:38

going to have to use our brains on this one

00:39

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

00:41

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

00:44

the diameter of this circle is ten centimeters which makes

00:46

the radius this thing right here Half that or five

00:49

centimeters were also told that the measure of the angle

00:52

is forty five degrees Him right there And the minor

00:55

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

00:58

looking for the area of this grayish section over here

01:02

So what do we do next Is it time to

01:03

use a lifeline waken do this because circles are our

01:07

jam We already know that circumference equals diameter times pi

01:11

making the circumference of this circle ten pie since the

01:15

arc x z is ten thirds pi or one third

01:18

of the total length the angle x y z must

01:21

be a third of the total angle measurement as well

01:23

which is always three hundred sixty degrees when dealing with

01:25

the circle one third of three sixty is one twenty

01:29

What this also means is that the area of the

01:31

unshaded part of the circle is gonna be exactly one

01:34

third of the area of the total circle While we

01:36

need to do now is find out the area of

01:38

the whole circle and then take two thirds of it

01:40

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

01:43

had the formula for the area of a circle grafted

01:45

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

01:48

gonna be pi times are square where are is the

01:51

radius The area will be pi times five squared and

01:55

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

01:58

pie piece of cake Finally you have to take two

02:01

thirds of the total area to get shaded portion twenty

02:03

five five times two thirds is fifty over three times

02:06

pi which is answer c thank very much Xy may

02:09

just be a minor arc but we have a feeling

02:11

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