Diameter

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ACT Math › Diameter

Questions 1 - 10
1

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.

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.

2

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.

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.

3

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

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.

4

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

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.

5

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

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,

6

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

36

18

6

3

72

Explanation

The perimeter of a circle = 2 πr = πd

Therefore d = 36

7

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

36

18

6

3

72

Explanation

The perimeter of a circle = 2 πr = πd

Therefore d = 36

8

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

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,

9

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

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 .

10

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

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 .

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