ACT Math : How to find the length of the diameter

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Length Of The Diameter

The perimeter of a circle is 36 π.  What is the diameter of the circle?

Possible Answers:

6

72

3

18

36

Correct answer:

36

Explanation:

The perimeter of a circle = 2 πr = πd

Therefore d = 36

Example Question #287 : Plane Geometry

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle? 

Possible Answers:

Correct answer:

Explanation:

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr2.

Example Question #1 : How To Find The Length Of The Diameter

If a circle has an area of , what is the diameter of the circle?

Possible Answers:

Correct answer:

Explanation:

1. Use the area to find the radius:

 

2. Use the radius to find the diameter:

 

Example Question #531 : Geometry

In a group of students, it was decided that a pizza would be divided according to its crust size. Every student wanted  inches of crust (measured from the outermost point of the pizza). If the pizza in question had a diameter of  , what percentage of the pizza was wasted by this manner of cutting the pizza? Round to the nearest hundredth.

Possible Answers:

Correct answer:

Explanation:

What we are looking at is a way of dividing the pizza according to arc lengths of the crust. Thus, we need to know the total circumference first. Since the diameter is , we know that the circumference is . Now, we want to ask how many ways we can divide up the pizza into pieces of  inch crust. This is:

 or approximately  pieces.

What you need to do is take this amount and subtract off . This is the amount of crust that is wasted. You can then merely divide it by the original amount of divisions:

(You do not need to work in exact area or length. These relative values work fine.) 

This is about  of the pizza that is wasted.

Example Question #531 : Plane Geometry

A circle has an area of  . What is its diameter?

Possible Answers:

 

 

 

 

 

Correct answer:

 

Explanation:

To solve a question like this, first remember that the area of a circle is defined as:

For your data, this is:

To solve for , first divide both sides by . Then take the square root of both sides. Thus you get:

The diameter of the circle is just double that:

Rounding to the nearest hundredth, you get .

Example Question #533 : Geometry

What is the diameter of a semi-circle that has an area of ?

Possible Answers:

Correct answer:

Explanation:

To begin, be very careful to note that the question asks about a semi-circle—not a complete circle! This means that a complete circle composed out of two of these semi-circles would have an area of . Now, from this, we can use our area formula, which is:

For our data, this is:

Solving for , we get:

This can be simplified to:

The diameter is , which is  or .

Example Question #2 : How To Find The Length Of The Diameter

A circle has an area of .  What is the diameter of the circle?  

Possible Answers:

Correct answer:

Explanation:

The equation for the area of a circle is , which in this case equals .  Therefore,  The only thing squared that equals an integer (which is not a perfect root) is that number under a square root.  Therefore, .  Since diameter is twice the radius, 

Example Question #533 : Plane Geometry

Find the diameter given the radius is .

Possible Answers:

Correct answer:

Explanation:

Diameter is simply twice the radius. Therefore, .

Example Question #536 : Geometry

Find the length of the diameter of a circle given the area is .

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a circle, solve for r, and multiply by 2 to get the diameter. Thus,

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