ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


Area Videos 3 videos

SAT Math 7.4 Geometry and Measurement
205 Views

SAT Math 7.4 Geometry and Measurement

SAT Math 1.1 Geometry and Measurement
719 Views

SAT Math 1.1 Geometry and Measurement. What is the circumference of the circle?

SAT Math 4.4 Geometry and Measurement
210 Views

SAT Math 4.4 Geometry and Measurement

See All

SAT Math 7.4 Geometry and Measurement 205 Views


Share It!


Description:

SAT Math 7.4 Geometry and Measurement


Transcript

00:02

Here’s your shmoop du jour, brought to you by a midpoint.

00:06

Apparently, it has some kind of restraining order against the circumference.

00:17

F is the midpoint of DG and E is the midpoint of FD.

00:21

What is the ratio of the area of the circle with center E to the area of the circle with center G?

00:29

Here are the potential answers...

00:33

Okay, so we’ve got three circles here…and we want to know how many of the itty-bitty

00:37

circles we could fit inside the big circle.

00:40

Well, all right…to be more technically accurate, we want a ratio of the area.

00:45

And all we can use to get there is a couple of midpoints.

00:48

These guys had better be good. Okay… here’s another problem where we’re

00:48

going to have to go ahead and just call something “x.”

00:48

In this case, we know that ED is a radius of the smallest circle… so we’ll call

00:53

that guy “x.”

00:54

That would make FD, the smallest circle's diameter, 2x.

00:59

And, because FD is also a radius of the medium circle…GD is going to be 4x.

01:05

Now that we have our radii, it’s time to whip out the formula for the area of a circle,

01:09

and go to work… For our smallest circle, we’ll take the formula

01:13

Area equals pi times r squared and plug in our… r…

01:20

…to get pi x squared.

01:22

For the big circle, we get pi times the quantity 4x… squared… or pi sixteen x squared.

01:28

We’re looking for the ratio, which is always the same as a fraction…

01:32

…and in this case is pi times x squared over pi times sixteen x squared.

01:38

The pi and the x squared cancel out…leaving us with just 1 over 16…

01:43

…which is equivalent to option A.

Related Videos

SAT Math 2.1 Geometry and Measurement
2779 Views

SAT Math 2.1 Geometry and Measurement. What is the measure of angle z in terms of x and y?

SAT Math 9.4 Algebra and Functions
1300 Views

SAT Math 9.4 Algebra and Functions

SAT Math 9.2 Algebra and Functions
377 Views

SAT Math 9.2 Algebra and Functions

SAT Math: Identifying an Equation for the Average of Two Percentages
23 Views

In 2014, the unemployment rate of one county in California was 7%. In another county, the unemployment rate was 11%. Which of the following express...

SAT Math: Which Equation Represents Profit?
13 Views

Angela is making cookies for a bake sale. She expects each batch of her cookies to sell for $40. It costs her $10 to make one batch of cookies, and...