ACT Math › Diameter
In a group of students, it was decided that a pizza would be divided according to its crust size. Every student wanted 3 inches of crust (measured from the outermost point of the pizza). If the pizza in question had a diameter of 14 inches, 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.
In a group of students, it was decided that a pizza would be divided according to its crust size. Every student wanted 3 inches of crust (measured from the outermost point of the pizza). If the pizza in question had a diameter of 14 inches, 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.
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.
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.
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,
The perimeter of a circle is 36 π. What is the diameter of the circle?
36
18
6
3
72
The perimeter of a circle = 2 πr = πd
Therefore d = 36
The perimeter of a circle is 36 π. What is the diameter of the circle?
36
18
6
3
72
The perimeter of a circle = 2 πr = πd
Therefore d = 36
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,
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 .
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 .