If the diameter of circle $C$ is $3$ time the diameter of circle $D$, then the area of one $C$ is how many times the area of one $D$ ?

So, you to be trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut climate you had some questions around the quant section—specifically concern 18 of ar 4 of practice Test 1. Those questions trial and error our expertise of Circles can be type of tricky, yet never fear, lungemine.com has gained your back!

Survey the Question

Let’s find the difficulty for clues as to what it will certainly be testing, together this will certainly help transition our minds come think about what form of math knowledge we’ll use to fix this question. Pay attention to any kind of words the sound math-specific and anything special around what the number look like, and mark them on your paper.

You are watching: If the diameter of circle c is 3 times the diameter of circle d

We have the right to see that we’re asked about circles, diameters, and also areas, so this question likely tests what we know about Circles. Let’s store this in mind as we proceed.

What execute We Know?

Let’s carefully read with the question and make a perform of the things that we know.

We desire to calculate the proportion of the area the one one to another circleWe understand the ratio of the diameters in between the 2 circles

Develop a Plan

Let’s begin with a top-down method to this question. We desire to know how many times larger the area of one $C$ is contrasted to the area of one $D$. Anytime we view the phrase “how numerous times larger,” we recognize that us are in search of the ratio the the two values in question. For this reason let’s walk ahead and also write the answer come this question as this ratio:

$$Area of Circle C/Area of Circle D$$

Next, we know that the area of a circle is $π(Radius)^2$, so let’s go ahead and plug the equation in for circle $C$ and also circle $D$.

$$Area of Circle C/Area of Circle D = π (Radius_C;)^2/π(Radius_D;)^2$$

We understand that the radius is simply the diameter that a circle separated by $2$. Therefore if the diameter of circle $C$ is three times larger than the diameter of circle $D$, climate the radius of circle $C$ is 3 times bigger than the radius of one $D$.

$$Radius_C = 3·Radius_D$$

So seems as if we have actually a clear path forward. We’ll just start substituting in equations, simplifying, and see what comes the end at the end.

Solve the Question

Let’s start with our ratio and also plug in $3·Radius_D$ for $Radius_C$:

$$Area of Circle C/Area of Circle D = π (3·Radius_D)^2/π(Radius_D)^2$$

Next, us can additional simplify this portion by canceling the end the $π$ and also $Radius_D$ native both the top and also bottom that the ideal fraction.

$$;;;;;;;;;;;;;;;;;;;;;;Area of Circle C/Area of Circle D = π (3·Radius_X)^2/π(Radius_X)^2$$$$;,Area of Circle C/Area of Circle D = 3^2$$$$Area of Circle C/Area of Circle D = 9$$

Well the wasn’t for this reason bad! us now have actually our final answer.

The exactly answer is $9$.

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What Did us Learn

When solving problems of the “how plenty of times bigger is Y than Z” variety, we have to start by creating a proportion for what the difficulty wants united state to solve. In this difficulty we began by composing the proportion of the area the one circle come the area of an additional circle:

$$Area of Circle C/Area of Circle D$$

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