All ACT Math Resources
Example Question #1 : Diameter And Chords
The perimeter of a circle is 36 π. What is the diameter of the circle?
The perimeter of a circle = 2 πr = πd
Therefore d = 36
Example Question #135 : Plane Geometry
Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?
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?
1. Use the area to find the radius:
2. Use the radius to find the diameter:
Example Question #531 : Plane 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.
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 #2 : How To Find The Length Of The Diameter
A circle has an area of . What is its diameter?
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 #62 : Circles
What is the diameter of a semi-circle that has an area of ?
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 #3 : How To Find The Length Of The Diameter
A circle has an area of . What is the diameter of the circle?
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 #64 : Circles
Find the diameter given the radius is .
Diameter is simply twice the radius. Therefore, .
Example Question #65 : Circles
Find the length of the diameter of a circle given the area is .
To solve, simply use the formula for the area of a circle, solve for r, and multiply by 2 to get the diameter. Thus,