PSAT 1.25 Math Diagnostic

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

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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